Question

(x – 9)^2 = (x + 1)^2

Answer 1

Are you aloud to just take the square root of both sides?

Answer 2

\[
(x – 9)^2 = (x + 1)^2 \\
(x – 9)^2 - (x + 1)^2 = 0 \\
\text{Since }a^2 - b^2 = (a+b)(a-b): \\
(x – 9)^2 - (x + 1)^2 = (x-9+x+1)(x-9-x-1) = 0 \\
(2x-8)(-10) = 0 \\
2x - 8 = 0 \\
2x = 8 \\
x = 8/2 = 4
\]

Answer 3

Another way to do this problem:
If a^2 = b^2 then either a = b OR a = -b
(x – 9)^2 = (x + 1)^2
x - 9 = x + 1 OR x - 9 = -x - 1
(no solution) OR x = -x - 1 + 9; x = -x + 8; 2x = 8; x = 4