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Simplifying 4(x + -1)(x + -1) = 9 Reorder the terms: 4(-1 + x)(x + -1) = 9 Reorder the terms: 4(-1 + x)(-1 + x) = 9 Multiply (-1 + x) * (-1 + x) 4(-1(-1 + x) + x(-1 + x)) = 9 4((-1 * -1 + x * -1) + x(-1 + x)) = 9 4((1 + -1x) + x(-1 + x)) = 9 4(1 + -1x + (-1 * x + x * x)) = 9 4(1 + -1x + (-1x + x2)) = 9 Combine like terms: -1x + -1x = -2x 4(1 + -2x + x2) = 9 (1 * 4 + -2x * 4 + x2 * 4) = 9 (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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