Question

For what values of x is x²-36=5x true?

a. -9 and -4
b. -4 and 9
c. 4 and -9
d. 9 and 4

Answer 1

To solve the equation x²-36=5x, rearrange the equation and apply the quadratic formula to find the solutions for x. The correct answer is -4 and 9.

Step-by-step explanation:

To solve the equation x²-36=5x, we need to bring all terms to one side of the equation to set it equal to zero. Rearranging the equation, we get x²-5x-36=0. Now, we can use the quadratic formula, which states that for an equation in the form ax²+bx+c=0, the solutions for x are given by:

x = (-b ± sqrt(b²-4ac)) / (2a)

For our equation, a=1, b=-5, and c=-36. Plugging these values into the quadratic formula, we get:

x = (-(-5) ± sqrt((-5)²-4(1)(-36))) / (2(1))

Simplifying further, we have:

x = (5 ± sqrt(25+144)) / 2

x = (5 ± sqrt(169)) / 2

x = (5 ± 13) / 2

So, the solutions for x are x = -4 and x = 9. Therefore, the correct answer is b. -4 and 9.