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Simplifying x2 + x2 + 2x + 1 = 25 Reorder the terms: 1 + 2x + x2 + x2 = 25 Combine like terms: x2 + x2 = 2x2 1 + 2x + 2x2 = 25 Solving 1 + 2x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: 1 + -25 + 2x + 2x2 = 25 + -25 Combine like terms: 1 + -25 = -24 -24 + 2x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -24 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
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 = 3Solution
x = {-4, 3}
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