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