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The equation of mathematical is the expression which encompassing the single (one) variable (that is unidentified value) and the “equal signs” (=) by the mathematical expression of every side of it. Its equal signs always articulate that the both sides are precisely having same values where the equation could also be very simple as x=0. The type of equation which is either false or true these are known as the identities;

Category: Engineering Paper Type: Online Exam | Quiz | Test Reference: APA Words: 2800

The equation which is obtained through the comparing to zero the sum of the finite number of terms every one of that is the multipolar of the positive integral power involving a power of zero of a different variables. The algebraic equation is defined as a statement of mathematical that has the two expressions where the set are equal to the each other. Now in the simple words its means the equality the sign of equal, and that the equation is all about the equating of one quantity with one another (Byjus.com, 2020).

Quadratic equation

In the algebra the equation of quadratic is the any equation which can be reorganized in the normal form as;

Whereas the x signifies the unidentified and the  represents the known numbers, and whereas then an equation is linear not the quadratic because have no term of . And it’s also has the number of a, b, c which are a coefficients of an equations and it might be notable through calling them.

To solve a quadratic equation this is a present in this form  and it’s also calculates the discriminant  and defined as  where the polynomials also has the real coefficients, and it has

·     Two distinct of the real roots has

·     One real of the double root has

·     There is no real root if  which has two complex conjugate roots (Laura Pennington, 2020)

Exponential equation

The exponential equation is the one where the variable happens in the form of exponents for examples   when on both side of equations has a same base and an exponents on an either side has the equal property if a  is the important logarithmic rules which is used to solve the exponential equations (Bryce S., 2019).

The function of exponential is the mathematical function in a below given form;

Whereas  the variable as well as  the constant which is also known as the base of function. And it is most usually met of the exponential function base which is an inspiring number and that is equal to 2.7182, so above expressions become as;

Simple algebraic equations Solution

Without brackets – Example with solution and checking

Example: 




As shown in the above example we the examples with the different signs and values without the brackets and we solved this example by applying using DMA’S rule.

Now if we checking this solution so put the value of  the given question if the both sides are equally then it’s true and correct solution

With brackets – Example with solution and checking


Solution 


Discussion

The above examples are about the simple algebraic equation with brackets; in this example first we take the examples from our self.  As shown in the above example we the examples with the different signs and values with the brackets and we solved this example by applying using the sequences of the brackets. (Your discussion should pinpoint exactly how it is as the explanation to your solution…why the answer is positive or negative[AJ1]  after the bracket is removed.  How did you get the solution?  Explain the specifics to your example. Your explanation is too general.)

Now if we checking this solution so put the value of  the given question if the both sides are equally then it’s true and correct solution

Example 2:


 [AJ1]It’s just a signs, brackets does not effect on this

So that signs which place is with greater is your correct sings

As shown in the above example we the examples with the different signs and values with the brackets and we solved this example by applying using the sequences of the brackets.

Now if we checking this solution so put the value of  the given question if the both sides are equally then it’s true and correct solution

Solution of the three basic methods in solving quadratic equation
Example with solution and checking of Factoring Methods

Example: 

Hence both prove that solution is correct

Discussion

The above example is the quadratic equation solving by the factoring method; in this method first of all equation should be equal to zero. Then we take the question as per requirements and solve this question by the factoring method. In this method the number is the totally factor a number into the prime factors which is positive where the prime number is that number which has the positive factor are the 1 as well as itself. In this solution the above quadratic equation is the standard quadratic equation. In this create the suitable pair which is fit in the given question and solve the complete question as shown in the above examples. Now we also solve the example by creating its quadratic equation as we present in the below example;

Example 2 


As shown in the above example 2 first we take the algebraic equation in the different arrangement, and then we set their arrangement in the form of the equation

   This is not equation[AJ1] .

Then we solve this equation by the factoring method as shown above, and also check their solution.

Example with solution and checking of Quadratic formula


 [AJ1]Standard Form of a Quadratic Equation looks like 

Example



Hence prove that;

Discussion

As shown in the above examples we apply the quadratic formula the example is correct because it’s shown in the checking both sides are equal.

Now the quadratic formula solution steps are given as follows; first write the equations in a general form of , as shown in the above question
. Then substitute a value of the  into the quadratic equation . (You need to explain where and how you get the value of a[AJ1] , b and c). The by applying a quadratic formula
 solve this question as shown in above examples. Then at last also check a solution of the quadratic equation by putting a value of

Example 2:

Used quadratic formula

 

Hence prove that;

Discussion

As shown in the above examples we apply the quadratic formula the example is correct because it’s shown in the checking both sides are equal.

Now the quadratic formula solution steps are given as follows; first write the equations in a general form of , as shown in the above question
. Then substitute the value of the  into the quadratic equation  Then by applying the quadratic formula  solve this question as shown in above examples. Then at last also check a solution of the quadratic equation by putting a value of

Example with solution and checking completing a square

Completing square example

Solution  


 [AJ1]This is standard form of

Now this is our equation   So;

a= 16; b = -12; c= -4


Discussion (Please explain the solution using completing the square)

As shown in the above examples we apply the completing square method the example is correct because it’s shown in the checking both sides are equal.

First we take the example of the algebraic equations as shown in the above examples by using the completing square method.  

solve we're going to go ahead and do this by completing the square so the first step and completing the square is to make sure that you only have X terms on one side so we'll start by taking 3 common and -12 from both sides and so we end up with 

Exponential equation Solution

Example with solution and checking With common base

Example:


Discussion

Consider the following exponential equation 3 rose to the X plus 2 is equal to 9 raised to the 2x minus 3. How can we find the value of x without using logs what you need to do is change base into base dream 3 squared is equal to 9. So we can replace 9 with 3 squared and whenever you raise one exponent to another exponent you need to multiply so we got to multiply 2 by  so on the right side this is going to be 3 raised to the . Now if the bases are the same and then the exponents must be equal to each other therefore  is equal to 4  now let's subtract both sides by X and let's add 6 to both sides so these 2 will cancel 2 plus 6 is 8  is 3x so we could see that X is equal to

Example with solution and checking Without common bases

Example:


Solution 


Discussion

Before we solve this problem since there is no possibility of getting a common base on both sides. As the left-hand side base is two whereas the right-hand side base is three. Therefore we have no choice but to use the logarithm. To solve this problem so let's go ahead and take a log on both sides I'm going to put a log on a left-hand side and log on a right-hand side. And now we will be using this fact this is  we're going to use to simplify this problem so over here in our case on a left hand side this is our exponent we are  going to move it to the front likewise  exponent we're going to move it to the front as well so then this problem is going to look like   times log of 2 equal to  times log of 3 let's go ahead and distribute log of 1 and X likewise over here so we're gonna get x times log2-1 times log of 2 is log of 2 and on the right hand side x times log of 3 plus 1 times log of 3 is log of 3. Now what we want to do is I want you to move this part x log of 3 on a left hand side and this negative log of two I want you to move in on a right hand side so this X log of two is already on a left hand side just leave it there. And this neck this X log of three becomes negative X log of three piece of cake n equals two we already have a lot of three on the right hand side and when you move negative log of two becomes positive log of two. 

So far so good look at the left-hand side we see X as a you can factor it out because X is common so I can put X outside and you put down log of two minus log of three equal to log of three plus log of two. Now what we want to do is we want to isolate X so that means we're gonna be dividing both sides by log of two minus log of three on this side. And likewise log of two minus log of three on this side so this whole thing is gone with this one so simply we ended up x equals true log of three plus log of 2 divided by log of two minus log of three.  Now the next step is use your calculator and figure out log of two and log of three and here I have already figured out log of two is approximately equal to 0.3 and log of 3 is approximately equal to 0.477 so let's plug it in those values right up here so X equal to log of three is 0.477 plus log of two is 0.3 divided by log of 2 is 0.3 -0.477 and if you simplify these ones that's gonna give you on the top 0.477 divided by negative 0.177 and if you divided that's gonna give you approximately equal to -4.4 so thus X is approximately equal to -4.4is answer.

Conclusion - Summary

Summing up all the discussion it is concluded that in this assignment that is about the quantitative analysis. In this assignment we solve the algebraic equation by using the different methods like the factoring method, completing square method and the last one method is the quadratic formula. In the simple algebraic equation which is containing the one variable (that is unknown value) and the “equal signs” (=) by the mathematical expression of every side of it. And the algebraic equation is defined as the statement of mathematical that has the two expressions where the set are equal to the each other. Now the quadratic equation rearranged in the standard form as;

To solve the quadratic equation this is the present in this form  and it’s also calculates the discriminant  and defined as  .Thus in the exponential equation is the one where the variable happens in the form of exponents for examples   when on both side of equations has a same base. All of requirements of this assignment are fulfilled.

References

Bryce S. (2019). What Is an Exponential Function? Retrieved from https://study.com/academy/lesson/whGEC4003 QM Writ 1 - L4B1 V1 Aug 2020at-is-an-exponential-function.html

Byjus.com. (2020). What are Algebraic Equations? Retrieved from https://byjus.com/maths/algebraic-equations/#:~:text=An%20algebraic%20equation%20can%20be,are%20like%20a%20balance%20scale.

Laura Pennington. (2020). Comparing Linear, Exponential & Quadratic Functions. Retrieved from https://study.com/academy/lesson/comparing-linear-exponential-quadratic-functions.html

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