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Simplifying 2x + 13 = 2x2 + 1 Reorder the terms: 13 + 2x = 2x2 + 1 Reorder the terms: 13 + 2x = 1 + 2x2 Solving 13 + 2x = 1 + 2x2 Solving for variable 'x'. Reorder the terms: 13 + -1 + 2x + -2x2 = 1 + 2x2 + -1 + -2x2 Combine like terms: 13 + -1 = 12 12 + 2x + -2x2 = 1 + 2x2 + -1 + -2x2 Reorder the terms: 12 + 2x + -2x2 = 1 + -1 + 2x2 + -2x2 Combine like terms: 1 + -1 = 0 12 + 2x + -2x2 = 0 + 2x2 + -2x2 12 + 2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + 2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + x + -1x2) = 0 Factor a trinomial. 2((3 + -1x)(2 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. 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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