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Simplifying (2x + -5)(2x + -5) + -1(x + -6)(x + -6) = 80 Reorder the terms: (-5 + 2x)(2x + -5) + -1(x + -6)(x + -6) = 80 Reorder the terms: (-5 + 2x)(-5 + 2x) + -1(x + -6)(x + -6) = 80 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) + -1(x + -6)(x + -6) = 80 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -1(x + -6)(x + -6) = 80 ((25 + -10x) + 2x * (-5 + 2x)) + -1(x + -6)(x + -6) = 80 (25 + -10x + (-5 * 2x + 2x * 2x)) + -1(x + -6)(x + -6) = 80 (25 + -10x + (-10x + 4x2)) + -1(x + -6)(x + -6) = 80 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) + -1(x + -6)(x + -6) = 80 Reorder the terms: 25 + -20x + 4x2 + -1(-6 + x)(x + -6) = 80 Reorder the terms: 25 + -20x + 4x2 + -1(-6 + x)(-6 + x) = 80 Multiply (-6 + x) * (-6 + x) 25 + -20x + 4x2 + -1(-6(-6 + x) + x(-6 + x)) = 80 25 + -20x + 4x2 + -1((-6 * -6 + x * -6) + x(-6 + x)) = 80 25 + -20x + 4x2 + -1((36 + -6x) + x(-6 + x)) = 80 25 + -20x + 4x2 + -1(36 + -6x + (-6 * x + x * x)) = 80 25 + -20x + 4x2 + -1(36 + -6x + (-6x + x2)) = 80 Combine like terms: -6x + -6x = -12x 25 + -20x + 4x2 + -1(36 + -12x + x2) = 80 25 + -20x + 4x2 + (36 * -1 + -12x * -1 + x2 * -1) = 80 25 + -20x + 4x2 + (-36 + 12x + -1x2) = 80 Reorder the terms: 25 + -36 + -20x + 12x + 4x2 + -1x2 = 80 Combine like terms: 25 + -36 = -11 -11 + -20x + 12x + 4x2 + -1x2 = 80 Combine like terms: -20x + 12x = -8x -11 + -8x + 4x2 + -1x2 = 80 Combine like terms: 4x2 + -1x2 = 3x2 -11 + -8x + 3x2 = 80 Solving -11 + -8x + 3x2 = 80 Solving for variable 'x'. Reorder the terms: -11 + -80 + -8x + 3x2 = 80 + -80 Combine like terms: -11 + -80 = -91 -91 + -8x + 3x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -91 + -8x + 3x2 = 0 Factor a trinomial. (-13 + -3x)(7 + -1x) = 0Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve: Simplifying -13 + -3x = 0 Solving -13 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -3x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3x = 0 + 13 -3x = 0 + 13 Combine like terms: 0 + 13 = 13 -3x = 13 Divide each side by '-3'. x = -4.333333333 Simplifying x = -4.333333333Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-4.333333333, 7}
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