Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B....

Question

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations does not require Step 1 of the method for completing the square described in this section. Which one is it? Solve it.

Accepted Answer

Hey, everyone here, we are asked to select one of the following equations which can be solved by skipping the first step in completing the square. And then we need to work out the values of X. So starting taking a look at equation one, we see that we actually have a quadratic equation. So our first step here would be either applying the quadratic formula or just factoring this expression to solve for X. Now looking that equation two, we see that we have a squared expression on the left hand side of our equation. So we know that we could apply the square root property to this equation in order to solve for X. And now jumping to our fourth equation here, we see we have a product of two expressions set equal to zero. So here we know we could apply the zero factor property. So with this, we are left with the equation three where we have X squared minus X is equal to 72. Now taking a look at this expression, we see that our first step in completing the square would be to divide both sides of the equation by the coefficient of X squared. Well, with the equation three, we see we do not have a coefficient for X squared. So we wouldn't have to do any dividing here. Additionally, There isn't any arranging rearranging that we have to do with this equation since we already have the constant 72 moved over to the right hand side. So with this, if we were to apply the first step of completing the square, we would just be left with this same equation. So with this, we know that we do not have to perform the first step in completing the square. So we can go ahead and just skip to working out the value of X. So we can begin by moving the constant over to the left hand side. So to do this, we just subtract 72 from both sides. So we are left with X squared minus X minus is equal to zero. And now all we have to do is factor the left side of the equation to find our values for X. So factoring we have the quantity of X plus eight times the quantity of X minus nine is equal to zero. And now we can set both individual expressions equal to zero to find our values for X. So first we set X plus eight equal to zero. And now solving for X, we just have to subtract eight from both sides. And we see one of our solutions for X is negative. Eight. And next, with the second part of our X expression where we have X minus nine. Again, we set this equal to zero and solving for X. All we need to do is add nine to both sides. And we see that the second solution we have for X is positive nine. So in summary, we have found two solutions for X from our third equation which are negative eight and nine. So with this again, with our third equation and our two solutions, we are left with answer choice. E thanks for watching. I hope you found this video helpful and I'll see you again next time.

Struggling with College Algebra?

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations does not require Step 1 of the method for completing the square described in this section. Which one is it? Solve it.

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