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Simplifying 4x + 7 = -2x2 + -8x + -3 Reorder the terms: 7 + 4x = -2x2 + -8x + -3 Reorder the terms: 7 + 4x = -3 + -8x + -2x2 Solving 7 + 4x = -3 + -8x + -2x2 Solving for variable 'x'. Reorder the terms: 7 + 3 + 4x + 8x + 2x2 = -3 + -8x + -2x2 + 3 + 8x + 2x2 Combine like terms: 7 + 3 = 10 10 + 4x + 8x + 2x2 = -3 + -8x + -2x2 + 3 + 8x + 2x2 Combine like terms: 4x + 8x = 12x 10 + 12x + 2x2 = -3 + -8x + -2x2 + 3 + 8x + 2x2 Reorder the terms: 10 + 12x + 2x2 = -3 + 3 + -8x + 8x + -2x2 + 2x2 Combine like terms: -3 + 3 = 0 10 + 12x + 2x2 = 0 + -8x + 8x + -2x2 + 2x2 10 + 12x + 2x2 = -8x + 8x + -2x2 + 2x2 Combine like terms: -8x + 8x = 0 10 + 12x + 2x2 = 0 + -2x2 + 2x2 10 + 12x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 10 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 6x + x2) = 0 Factor a trinomial. 2((5 + x)(1 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-5, -1}
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