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Simplifying 169 = x2 + x2 + 14x + 49 Reorder the terms: 169 = 49 + 14x + x2 + x2 Combine like terms: x2 + x2 = 2x2 169 = 49 + 14x + 2x2 Solving 169 = 49 + 14x + 2x2 Solving for variable 'x'. Combine like terms: 169 + -49 = 120 120 + -14x + -2x2 = 49 + 14x + 2x2 + -49 + -14x + -2x2 Reorder the terms: 120 + -14x + -2x2 = 49 + -49 + 14x + -14x + 2x2 + -2x2 Combine like terms: 49 + -49 = 0 120 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2 120 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 120 + -14x + -2x2 = 0 + 2x2 + -2x2 120 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 120 + -14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -7x + -1x2) = 0 Factor a trinomial. 2((5 + -1x)(12 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {5, -12}
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