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Simplifying (x + -2)(x + -2) + -1(2x + 3)(2x + 3) = -80 Reorder the terms: (-2 + x)(x + -2) + -1(2x + 3)(2x + 3) = -80 Reorder the terms: (-2 + x)(-2 + x) + -1(2x + 3)(2x + 3) = -80 Multiply (-2 + x) * (-2 + x) (-2(-2 + x) + x(-2 + x)) + -1(2x + 3)(2x + 3) = -80 ((-2 * -2 + x * -2) + x(-2 + x)) + -1(2x + 3)(2x + 3) = -80 ((4 + -2x) + x(-2 + x)) + -1(2x + 3)(2x + 3) = -80 (4 + -2x + (-2 * x + x * x)) + -1(2x + 3)(2x + 3) = -80 (4 + -2x + (-2x + x2)) + -1(2x + 3)(2x + 3) = -80 Combine like terms: -2x + -2x = -4x (4 + -4x + x2) + -1(2x + 3)(2x + 3) = -80 Reorder the terms: 4 + -4x + x2 + -1(3 + 2x)(2x + 3) = -80 Reorder the terms: 4 + -4x + x2 + -1(3 + 2x)(3 + 2x) = -80 Multiply (3 + 2x) * (3 + 2x) 4 + -4x + x2 + -1(3(3 + 2x) + 2x * (3 + 2x)) = -80 4 + -4x + x2 + -1((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = -80 4 + -4x + x2 + -1((9 + 6x) + 2x * (3 + 2x)) = -80 4 + -4x + x2 + -1(9 + 6x + (3 * 2x + 2x * 2x)) = -80 4 + -4x + x2 + -1(9 + 6x + (6x + 4x2)) = -80 Combine like terms: 6x + 6x = 12x 4 + -4x + x2 + -1(9 + 12x + 4x2) = -80 4 + -4x + x2 + (9 * -1 + 12x * -1 + 4x2 * -1) = -80 4 + -4x + x2 + (-9 + -12x + -4x2) = -80 Reorder the terms: 4 + -9 + -4x + -12x + x2 + -4x2 = -80 Combine like terms: 4 + -9 = -5 -5 + -4x + -12x + x2 + -4x2 = -80 Combine like terms: -4x + -12x = -16x -5 + -16x + x2 + -4x2 = -80 Combine like terms: x2 + -4x2 = -3x2 -5 + -16x + -3x2 = -80 Solving -5 + -16x + -3x2 = -80 Solving for variable 'x'. Reorder the terms: -5 + 80 + -16x + -3x2 = -80 + 80 Combine like terms: -5 + 80 = 75 75 + -16x + -3x2 = -80 + 80 Combine like terms: -80 + 80 = 0 75 + -16x + -3x2 = 0 Factor a trinomial. (3 + -1x)(25 + 3x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(25 + 3x)' equal to zero and attempt to solve: Simplifying 25 + 3x = 0 Solving 25 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 3x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 3x = 0 + -25 3x = 0 + -25 Combine like terms: 0 + -25 = -25 3x = -25 Divide each side by '3'. x = -8.333333333 Simplifying x = -8.333333333Solution
x = {3, -8.333333333}
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