how to solve (x+a)(x+b)=27

Question

Suppose you are given the equation of the form (x+a)(x+b)=27 where a and b are real numbers. Explain how you would solve this.

Answer 1

Your solution will be in terms of a and b. We can start by expanding:

(x+a)(x+b)-27 = 0

x^2+(a+b)x+ab-27 = 0.

Then, using the quadratic formula,

x = [-(a+b)±sqrt((a+b)^2-4(ab-27))]/2.