Find the exact solution of the following quadratic equation by using the Quadratic Formula. x^2-9x=36

x = 12 or x = - 3

Step-by-step explanation:

Solve for x over the real numbers:

x^2 - 9 x = 36

Subtract 36 from both sides:

x^2 - 9 x - 36 = 0

x = (9 ± sqrt ((-9) ^2 - 4 (-36))) / 2 = (9 ± sqrt (81 + 144)) / 2 = (9 ± sqrt (225)) / 2:

x = (9 + sqrt (225)) / 2 or x = (9 - sqrt (225)) / 2

sqrt (225) = sqrt (9*25) = sqrt (3^2*5^2) = 3*5 = 15:

x = (9 + 15) / 2 or x = (9 - 15) / 2

(9 + 15) / 2 = 24/2 = 12:

x = 12 or x = (9 - 15) / 2

(9 - 15) / 2 = - 6/2 = - 3:

Answer: x = 12 or x = - 3