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