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Simplifying x + 7 + -1(x + -3)(x + 5) = 3x + 26 Reorder the terms: x + 7 + -1(-3 + x)(x + 5) = 3x + 26 Reorder the terms: x + 7 + -1(-3 + x)(5 + x) = 3x + 26 Multiply (-3 + x) * (5 + x) x + 7 + -1(-3(5 + x) + x(5 + x)) = 3x + 26 x + 7 + -1((5 * -3 + x * -3) + x(5 + x)) = 3x + 26 x + 7 + -1((-15 + -3x) + x(5 + x)) = 3x + 26 x + 7 + -1(-15 + -3x + (5 * x + x * x)) = 3x + 26 x + 7 + -1(-15 + -3x + (5x + x2)) = 3x + 26 Combine like terms: -3x + 5x = 2x x + 7 + -1(-15 + 2x + x2) = 3x + 26 x + 7 + (-15 * -1 + 2x * -1 + x2 * -1) = 3x + 26 x + 7 + (15 + -2x + -1x2) = 3x + 26 Reorder the terms: 7 + 15 + x + -2x + -1x2 = 3x + 26 Combine like terms: 7 + 15 = 22 22 + x + -2x + -1x2 = 3x + 26 Combine like terms: x + -2x = -1x 22 + -1x + -1x2 = 3x + 26 Reorder the terms: 22 + -1x + -1x2 = 26 + 3x Solving 22 + -1x + -1x2 = 26 + 3x Solving for variable 'x'. Reorder the terms: 22 + -26 + -1x + -3x + -1x2 = 26 + 3x + -26 + -3x Combine like terms: 22 + -26 = -4 -4 + -1x + -3x + -1x2 = 26 + 3x + -26 + -3x Combine like terms: -1x + -3x = -4x -4 + -4x + -1x2 = 26 + 3x + -26 + -3x Reorder the terms: -4 + -4x + -1x2 = 26 + -26 + 3x + -3x Combine like terms: 26 + -26 = 0 -4 + -4x + -1x2 = 0 + 3x + -3x -4 + -4x + -1x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -4 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 4x + x2) = 0 Factor a trinomial. -1((2 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2, -2}
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