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Simplifying 522 = 2x2 + 16x + 312 Reorder the terms: 522 = 312 + 16x + 2x2 Solving 522 = 312 + 16x + 2x2 Solving for variable 'x'. Combine like terms: 522 + -312 = 210 210 + -16x + -2x2 = 312 + 16x + 2x2 + -312 + -16x + -2x2 Reorder the terms: 210 + -16x + -2x2 = 312 + -312 + 16x + -16x + 2x2 + -2x2 Combine like terms: 312 + -312 = 0 210 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2 210 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 210 + -16x + -2x2 = 0 + 2x2 + -2x2 210 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 210 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(105 + -8x + -1x2) = 0 Factor a trinomial. 2((7 + -1x)(15 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 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 = {7, -15}
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