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