Final answer:
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.