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Simplifying -1(x + 5)(x + 5) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) Reorder the terms: -1(5 + x)(x + 5) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) Reorder the terms: -1(5 + x)(5 + x) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) Multiply (5 + x) * (5 + x) -1(5(5 + x) + x(5 + x)) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) -1((5 * 5 + x * 5) + x(5 + x)) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) -1((25 + 5x) + x(5 + x)) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) -1(25 + 5x + (5 * x + x * x)) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) -1(25 + 5x + (5x + x2)) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) Combine like terms: 5x + 5x = 10x -1(25 + 10x + x2) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) (25 * -1 + 10x * -1 + x2 * -1) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) (-25 + -10x + -1x2) + (x + -4)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) Reorder the terms: -25 + -10x + -1x2 + (-4 + x)(x + -4) + 5(2x + 5) = -5(x + 2)(x + -2) Reorder the terms: -25 + -10x + -1x2 + (-4 + x)(-4 + x) + 5(2x + 5) = -5(x + 2)(x + -2) Multiply (-4 + x) * (-4 + x) -25 + -10x + -1x2 + (-4(-4 + x) + x(-4 + x)) + 5(2x + 5) = -5(x + 2)(x + -2) -25 + -10x + -1x2 + ((-4 * -4 + x * -4) + x(-4 + x)) + 5(2x + 5) = -5(x + 2)(x + -2) -25 + -10x + -1x2 + ((16 + -4x) + x(-4 + x)) + 5(2x + 5) = -5(x + 2)(x + -2) -25 + -10x + -1x2 + (16 + -4x + (-4 * x + x * x)) + 5(2x + 5) = -5(x + 2)(x + -2) -25 + -10x + -1x2 + (16 + -4x + (-4x + x2)) + 5(2x + 5) = -5(x + 2)(x + -2) Combine like terms: -4x + -4x = -8x -25 + -10x + -1x2 + (16 + -8x + x2) + 5(2x + 5) = -5(x + 2)(x + -2) Reorder the terms: -25 + -10x + -1x2 + 16 + -8x + x2 + 5(5 + 2x) = -5(x + 2)(x + -2) -25 + -10x + -1x2 + 16 + -8x + x2 + (5 * 5 + 2x * 5) = -5(x + 2)(x + -2) -25 + -10x + -1x2 + 16 + -8x + x2 + (25 + 10x) = -5(x + 2)(x + -2) Reorder the terms: -25 + 16 + 25 + -10x + -8x + 10x + -1x2 + x2 = -5(x + 2)(x + -2) Combine like terms: -25 + 16 = -9 -9 + 25 + -10x + -8x + 10x + -1x2 + x2 = -5(x + 2)(x + -2) Combine like terms: -9 + 25 = 16 16 + -10x + -8x + 10x + -1x2 + x2 = -5(x + 2)(x + -2) Combine like terms: -10x + -8x = -18x 16 + -18x + 10x + -1x2 + x2 = -5(x + 2)(x + -2) Combine like terms: -18x + 10x = -8x 16 + -8x + -1x2 + x2 = -5(x + 2)(x + -2) Combine like terms: -1x2 + x2 = 0 16 + -8x + 0 = -5(x + 2)(x + -2) 16 + -8x = -5(x + 2)(x + -2) Reorder the terms: 16 + -8x = -5(2 + x)(x + -2) Reorder the terms: 16 + -8x = -5(2 + x)(-2 + x) Multiply (2 + x) * (-2 + x) 16 + -8x = -5(2(-2 + x) + x(-2 + x)) 16 + -8x = -5((-2 * 2 + x * 2) + x(-2 + x)) 16 + -8x = -5((-4 + 2x) + x(-2 + x)) 16 + -8x = -5(-4 + 2x + (-2 * x + x * x)) 16 + -8x = -5(-4 + 2x + (-2x + x2)) Combine like terms: 2x + -2x = 0 16 + -8x = -5(-4 + 0 + x2) 16 + -8x = -5(-4 + x2) 16 + -8x = (-4 * -5 + x2 * -5) 16 + -8x = (20 + -5x2) Solving 16 + -8x = 20 + -5x2 Solving for variable 'x'. Reorder the terms: 16 + -20 + -8x + 5x2 = 20 + -5x2 + -20 + 5x2 Combine like terms: 16 + -20 = -4 -4 + -8x + 5x2 = 20 + -5x2 + -20 + 5x2 Reorder the terms: -4 + -8x + 5x2 = 20 + -20 + -5x2 + 5x2 Combine like terms: 20 + -20 = 0 -4 + -8x + 5x2 = 0 + -5x2 + 5x2 -4 + -8x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -4 + -8x + 5x2 = 0 Factor a trinomial. (-2 + -5x)(2 + -1x) = 0Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-0.4, 2}
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