Find all values of x such that x/(x + 4) = -9/(x + 5). If you find more than one value, then list your solutions in increasing order, separated by commas.
+128460 x / (x +4) = -9 /( x + 5) cross-multiply
x ( x + 5) = -9 ( x + 4) simplify
x^2 + 5x = -9x - 36 rearrange as
x^2 + 14x + 36 = 0 complete the square on x
x^2 + 14x = -36 take 1/2 of 14 =7.....square this = 49....add to both sides
x^2 + 14x + 49 = -36 + 49 factor the left, simplify the right
(x + 7)^2 = 13 take both roots
x+ 7 = sqrt (13) or x + 7 = -sqrt (13)
x = sqrt (13) - 7 or x = -sqrt (13) - 7
