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Simplifying x + 7 = x2 + 9x + 19 Reorder the terms: 7 + x = x2 + 9x + 19 Reorder the terms: 7 + x = 19 + 9x + x2 Solving 7 + x = 19 + 9x + x2 Solving for variable 'x'. Reorder the terms: 7 + -19 + x + -9x + -1x2 = 19 + 9x + x2 + -19 + -9x + -1x2 Combine like terms: 7 + -19 = -12 -12 + x + -9x + -1x2 = 19 + 9x + x2 + -19 + -9x + -1x2 Combine like terms: x + -9x = -8x -12 + -8x + -1x2 = 19 + 9x + x2 + -19 + -9x + -1x2 Reorder the terms: -12 + -8x + -1x2 = 19 + -19 + 9x + -9x + x2 + -1x2 Combine like terms: 19 + -19 = 0 -12 + -8x + -1x2 = 0 + 9x + -9x + x2 + -1x2 -12 + -8x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 -12 + -8x + -1x2 = 0 + x2 + -1x2 -12 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 8x + x2) = 0 Factor a trinomial. -1((6 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 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 = {-6, -2}
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