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Simplifying (2x + -1)(2x + -1) + -1(x + -5)(2x + -1) = 0 Reorder the terms: (-1 + 2x)(2x + -1) + -1(x + -5)(2x + -1) = 0 Reorder the terms: (-1 + 2x)(-1 + 2x) + -1(x + -5)(2x + -1) = 0 Multiply (-1 + 2x) * (-1 + 2x) (-1(-1 + 2x) + 2x * (-1 + 2x)) + -1(x + -5)(2x + -1) = 0 ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + -1(x + -5)(2x + -1) = 0 ((1 + -2x) + 2x * (-1 + 2x)) + -1(x + -5)(2x + -1) = 0 (1 + -2x + (-1 * 2x + 2x * 2x)) + -1(x + -5)(2x + -1) = 0 (1 + -2x + (-2x + 4x2)) + -1(x + -5)(2x + -1) = 0 Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) + -1(x + -5)(2x + -1) = 0 Reorder the terms: 1 + -4x + 4x2 + -1(-5 + x)(2x + -1) = 0 Reorder the terms: 1 + -4x + 4x2 + -1(-5 + x)(-1 + 2x) = 0 Multiply (-5 + x) * (-1 + 2x) 1 + -4x + 4x2 + -1(-5(-1 + 2x) + x(-1 + 2x)) = 0 1 + -4x + 4x2 + -1((-1 * -5 + 2x * -5) + x(-1 + 2x)) = 0 1 + -4x + 4x2 + -1((5 + -10x) + x(-1 + 2x)) = 0 1 + -4x + 4x2 + -1(5 + -10x + (-1 * x + 2x * x)) = 0 1 + -4x + 4x2 + -1(5 + -10x + (-1x + 2x2)) = 0 Combine like terms: -10x + -1x = -11x 1 + -4x + 4x2 + -1(5 + -11x + 2x2) = 0 1 + -4x + 4x2 + (5 * -1 + -11x * -1 + 2x2 * -1) = 0 1 + -4x + 4x2 + (-5 + 11x + -2x2) = 0 Reorder the terms: 1 + -5 + -4x + 11x + 4x2 + -2x2 = 0 Combine like terms: 1 + -5 = -4 -4 + -4x + 11x + 4x2 + -2x2 = 0 Combine like terms: -4x + 11x = 7x -4 + 7x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -4 + 7x + 2x2 = 0 Solving -4 + 7x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-4 + -1x)(1 + -2x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
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 = 0.5Solution
x = {-4, 0.5}
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