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Simplifying 289 = 2x2 + 14x + 49 Reorder the terms: 289 = 49 + 14x + 2x2 Solving 289 = 49 + 14x + 2x2 Solving for variable 'x'. Combine like terms: 289 + -49 = 240 240 + -14x + -2x2 = 49 + 14x + 2x2 + -49 + -14x + -2x2 Reorder the terms: 240 + -14x + -2x2 = 49 + -49 + 14x + -14x + 2x2 + -2x2 Combine like terms: 49 + -49 = 0 240 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2 240 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 240 + -14x + -2x2 = 0 + 2x2 + -2x2 240 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 240 + -14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(120 + -7x + -1x2) = 0 Factor a trinomial. 2((8 + -1x)(15 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {8, -15}
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