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Simplifying (3x + -3)(3x + -3) + 33x = (2x + -2)(2x + -2) + -19 Reorder the terms: (-3 + 3x)(3x + -3) + 33x = (2x + -2)(2x + -2) + -19 Reorder the terms: (-3 + 3x)(-3 + 3x) + 33x = (2x + -2)(2x + -2) + -19 Multiply (-3 + 3x) * (-3 + 3x) (-3(-3 + 3x) + 3x * (-3 + 3x)) + 33x = (2x + -2)(2x + -2) + -19 ((-3 * -3 + 3x * -3) + 3x * (-3 + 3x)) + 33x = (2x + -2)(2x + -2) + -19 ((9 + -9x) + 3x * (-3 + 3x)) + 33x = (2x + -2)(2x + -2) + -19 (9 + -9x + (-3 * 3x + 3x * 3x)) + 33x = (2x + -2)(2x + -2) + -19 (9 + -9x + (-9x + 9x2)) + 33x = (2x + -2)(2x + -2) + -19 Combine like terms: -9x + -9x = -18x (9 + -18x + 9x2) + 33x = (2x + -2)(2x + -2) + -19 Reorder the terms: 9 + -18x + 33x + 9x2 = (2x + -2)(2x + -2) + -19 Combine like terms: -18x + 33x = 15x 9 + 15x + 9x2 = (2x + -2)(2x + -2) + -19 Reorder the terms: 9 + 15x + 9x2 = (-2 + 2x)(2x + -2) + -19 Reorder the terms: 9 + 15x + 9x2 = (-2 + 2x)(-2 + 2x) + -19 Multiply (-2 + 2x) * (-2 + 2x) 9 + 15x + 9x2 = (-2(-2 + 2x) + 2x * (-2 + 2x)) + -19 9 + 15x + 9x2 = ((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) + -19 9 + 15x + 9x2 = ((4 + -4x) + 2x * (-2 + 2x)) + -19 9 + 15x + 9x2 = (4 + -4x + (-2 * 2x + 2x * 2x)) + -19 9 + 15x + 9x2 = (4 + -4x + (-4x + 4x2)) + -19 Combine like terms: -4x + -4x = -8x 9 + 15x + 9x2 = (4 + -8x + 4x2) + -19 Reorder the terms: 9 + 15x + 9x2 = 4 + -19 + -8x + 4x2 Combine like terms: 4 + -19 = -15 9 + 15x + 9x2 = -15 + -8x + 4x2 Solving 9 + 15x + 9x2 = -15 + -8x + 4x2 Solving for variable 'x'. Reorder the terms: 9 + 15 + 15x + 8x + 9x2 + -4x2 = -15 + -8x + 4x2 + 15 + 8x + -4x2 Combine like terms: 9 + 15 = 24 24 + 15x + 8x + 9x2 + -4x2 = -15 + -8x + 4x2 + 15 + 8x + -4x2 Combine like terms: 15x + 8x = 23x 24 + 23x + 9x2 + -4x2 = -15 + -8x + 4x2 + 15 + 8x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 24 + 23x + 5x2 = -15 + -8x + 4x2 + 15 + 8x + -4x2 Reorder the terms: 24 + 23x + 5x2 = -15 + 15 + -8x + 8x + 4x2 + -4x2 Combine like terms: -15 + 15 = 0 24 + 23x + 5x2 = 0 + -8x + 8x + 4x2 + -4x2 24 + 23x + 5x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 24 + 23x + 5x2 = 0 + 4x2 + -4x2 24 + 23x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 24 + 23x + 5x2 = 0 Factor a trinomial. (3 + x)(8 + 5x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(8 + 5x)' equal to zero and attempt to solve: Simplifying 8 + 5x = 0 Solving 8 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5x = 0 + -8 5x = 0 + -8 Combine like terms: 0 + -8 = -8 5x = -8 Divide each side by '5'. x = -1.6 Simplifying x = -1.6Solution
x = {-3, -1.6}
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