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Simplifying x2 + x2 + 16x + 64 = 1600 Reorder the terms: 64 + 16x + x2 + x2 = 1600 Combine like terms: x2 + x2 = 2x2 64 + 16x + 2x2 = 1600 Solving 64 + 16x + 2x2 = 1600 Solving for variable 'x'. Reorder the terms: 64 + -1600 + 16x + 2x2 = 1600 + -1600 Combine like terms: 64 + -1600 = -1536 -1536 + 16x + 2x2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -1536 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-768 + 8x + x2) = 0 Factor a trinomial. 2((-32 + -1x)(24 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + -1x)' equal to zero and attempt to solve: Simplifying -32 + -1x = 0 Solving -32 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -1x = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -1x = 0 + 32 -1x = 0 + 32 Combine like terms: 0 + 32 = 32 -1x = 32 Divide each side by '-1'. x = -32 Simplifying x = -32Subproblem 2
Set the factor '(24 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Divide each side by '-1'. x = 24 Simplifying x = 24Solution
x = {-32, 24}
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