X2 + 17x - 12 = - 84

Step-by-step explanation:

The given quadratic equation is expressed as

x^2 + 17x - 12 = - 84

Adding - 84 to the left hand side and the right hand side of the equation, it becomes

x^2 + 17x - 12 + 84 = - 84 + 84.

x^2 + 17x + 72 = 0

We would find two numbers such that their sum or difference is 17x and their product is 72x^2. The two numbers are 8x and 9x. Therefore

x^2 + 8x + 9x + 72 = 0

x (x + 8) + 9 (x + 8) = 0

x + 9 = 0 or x + 8 = 0

x - 9 or x = 8