Find all values of x such that 2x/(x - 2) = -6/(x + 4).
If you find more than one value, then list your solutions, separated by commas.
+128408 2x / ( x - 2) = -6/ ( x + 4) cross-multiply
2x ( x + 4) = -6 ( x - 2) simplify
2x^2 + 8x = -6x + 12 rearrange as
2x^2 + 14x - 12 = 0 divide through by 2
x^2 + 7x - 6 = 0 add 6 to both sides
x^2 + 7x = 6
Complete the square on x
Take 1/2 of 7 = 7/2 square this = 49/4and add to both sides
x^2 + 7x + 49/4 = 6 + 49/4 factor the left side, simplify the right
(x + 7/2)^2 = 73/4 take both roots
x + 7/2 = ±√73/2 subtract 7/2 from both sides
x = ±√73/2 - 7/2
