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Simplifying 4x2 + 16x + 16 = 40000 Reorder the terms: 16 + 16x + 4x2 = 40000 Solving 16 + 16x + 4x2 = 40000 Solving for variable 'x'. Reorder the terms: 16 + -40000 + 16x + 4x2 = 40000 + -40000 Combine like terms: 16 + -40000 = -39984 -39984 + 16x + 4x2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -39984 + 16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9996 + 4x + x2) = 0 Factor a trinomial. 4((-102 + -1x)(98 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-102 + -1x)' equal to zero and attempt to solve: Simplifying -102 + -1x = 0 Solving -102 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '102' to each side of the equation. -102 + 102 + -1x = 0 + 102 Combine like terms: -102 + 102 = 0 0 + -1x = 0 + 102 -1x = 0 + 102 Combine like terms: 0 + 102 = 102 -1x = 102 Divide each side by '-1'. x = -102 Simplifying x = -102Subproblem 2
Set the factor '(98 + -1x)' equal to zero and attempt to solve: Simplifying 98 + -1x = 0 Solving 98 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-98' to each side of the equation. 98 + -98 + -1x = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -1x = 0 + -98 -1x = 0 + -98 Combine like terms: 0 + -98 = -98 -1x = -98 Divide each side by '-1'. x = 98 Simplifying x = 98Solution
x = {-102, 98}
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