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Simplifying 100 = -16x2 + 32x + 100 Reorder the terms: 100 = 100 + 32x + -16x2 Add '-100' to each side of the equation. 100 + -100 = 100 + 32x + -100 + -16x2 Combine like terms: 100 + -100 = 0 0 = 100 + 32x + -100 + -16x2 Reorder the terms: 0 = 100 + -100 + 32x + -16x2 Combine like terms: 100 + -100 = 0 0 = 0 + 32x + -16x2 0 = 32x + -16x2 Solving 0 = 32x + -16x2 Solving for variable 'x'. Remove the zero: -32x + 16x2 = 32x + -16x2 + -32x + 16x2 Reorder the terms: -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -32x + 16x2 = 0 + -16x2 + 16x2 -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16x'. 16x(-2 + x) = 0 Ignore the factor 16.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {0, 2}
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