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Simplifying (2 + -2x)(2 + -2x) = 9 Multiply (2 + -2x) * (2 + -2x) (2(2 + -2x) + -2x * (2 + -2x)) = 9 ((2 * 2 + -2x * 2) + -2x * (2 + -2x)) = 9 ((4 + -4x) + -2x * (2 + -2x)) = 9 (4 + -4x + (2 * -2x + -2x * -2x)) = 9 (4 + -4x + (-4x + 4x2)) = 9 Combine like terms: -4x + -4x = -8x (4 + -8x + 4x2) = 9 Solving 4 + -8x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: 4 + -9 + -8x + 4x2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + -8x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + -8x + 4x2 = 0 Factor a trinomial. (-1 + -2x)(5 + -2x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-0.5, 2.5}
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