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Simplifying x + 5 = x2 + 5x + -7 Reorder the terms: 5 + x = x2 + 5x + -7 Reorder the terms: 5 + x = -7 + 5x + x2 Solving 5 + x = -7 + 5x + x2 Solving for variable 'x'. Reorder the terms: 5 + 7 + x + -5x + -1x2 = -7 + 5x + x2 + 7 + -5x + -1x2 Combine like terms: 5 + 7 = 12 12 + x + -5x + -1x2 = -7 + 5x + x2 + 7 + -5x + -1x2 Combine like terms: x + -5x = -4x 12 + -4x + -1x2 = -7 + 5x + x2 + 7 + -5x + -1x2 Reorder the terms: 12 + -4x + -1x2 = -7 + 7 + 5x + -5x + x2 + -1x2 Combine like terms: -7 + 7 = 0 12 + -4x + -1x2 = 0 + 5x + -5x + x2 + -1x2 12 + -4x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 12 + -4x + -1x2 = 0 + x2 + -1x2 12 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + -4x + -1x2 = 0 Factor a trinomial. (2 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
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 = -6Solution
x = {2, -6}
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