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Simplifying 0 = x2 + 47x + 522 Reorder the terms: 0 = 522 + 47x + x2 Solving 0 = 522 + 47x + x2 Solving for variable 'x'. Combine like terms: 0 + -522 = -522 -522 + -47x + -1x2 = 522 + 47x + x2 + -522 + -47x + -1x2 Reorder the terms: -522 + -47x + -1x2 = 522 + -522 + 47x + -47x + x2 + -1x2 Combine like terms: 522 + -522 = 0 -522 + -47x + -1x2 = 0 + 47x + -47x + x2 + -1x2 -522 + -47x + -1x2 = 47x + -47x + x2 + -1x2 Combine like terms: 47x + -47x = 0 -522 + -47x + -1x2 = 0 + x2 + -1x2 -522 + -47x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -522 + -47x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(522 + 47x + x2) = 0 Factor a trinomial. -1((29 + x)(18 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + x)' equal to zero and attempt to solve: Simplifying 29 + x = 0 Solving 29 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + x = 0 + -29 x = 0 + -29 Combine like terms: 0 + -29 = -29 x = -29 Simplifying x = -29Subproblem 2
Set the factor '(18 + x)' equal to zero and attempt to solve: Simplifying 18 + x = 0 Solving 18 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + x = 0 + -18 x = 0 + -18 Combine like terms: 0 + -18 = -18 x = -18 Simplifying x = -18Solution
x = {-29, -18}
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