Question

Find the solutions to the equation below. 9x^2 -81 = 0

Answer 1

$9x^2 -81 = 0 \\ x^2-9=0\\ x^2=9\\ x=-3 \vee x=3$

Answer 2

The solutions to the equation are +3 and -3.

This equation is called a perfect square binomial because it can be factored as a difference of two squares. To solve, first, you have to factor out like terms. In this case, you would factor out a 9 from the equation. Then, solve for X.

9x² - 81 = 0
9(x² - 9) = 0
x² - 9 + 9 = 0 + 9
√x² = √9
x = +3, -3