Exercises 137–139 will help you prepare for the material covered ...

Question

Exercises 137–139 will help you prepare for the material covered in the next section.Solve: x(x - 7) = 3.

Accepted Answer

Hello today we're going to be solving for X in the following equation. The equation given to us is X times x minus five is equal to eight. Now what I'm going to go ahead and do is distribute X into the quantity X minus five. And that's going to give me x squared minus five. X is equal to eight. Now since I want to solve for X I need to set this equation equal to zero. And in order to do that I can subtract eight to both sides of the equation and that's going to give me x squared minus five. X minus eight is equal to zero. Now with this is not a fact. Herbal try nominal but we could solve for X using the quadratic formula. So we need to go ahead and identify what our coefficients are. While the coefficients is A is equal to one. B. Is equal to negative five and C is equal to negative eight. And the quadratic formula states that X is equal to negative B plus or minus the square root of B squared minus four A. C. All over two. A. So we're gonna take our give our given coefficients and plug it into our quadratic formula. So doing so is going to give me X. Is equal to negative B which is negative negative five or positive five plus or minus the square root of negative five squared minus four times A. Which is one times C. Which is negative eight. All over two times a. Which is two times 1. So let's go ahead and simplify this. Well negative five squared is going to give us 25 so we have five plus or minus the square root of 25 negative four times one is negative four and negative four times eight is going to give us 32. So we have 25 plus 32 and two times one is going to give us two Now 25 plus 32 is going to give us 57 so X is equal to five plus or minus the square root of 57/2 and 57 can be rewritten well actually cannot be rewritten because it is a prime number. So this is the simplest form of X. But there are two values of X here because it's plus or minus. So X is equal to five plus the square root of 57/2 and X is equal to five minus the square root of 57/2. And these are going to be the values of X and the solution to our problem. And that means that the solution to this answer is going to be be So I hope this video helps you in understanding how to solve this type of equation. And I'll go ahead and see you all in the next video

Struggling with College Algebra?

Exercises 137–139 will help you prepare for the material covered in the next section.Solve: x(x - 7) = 3.

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