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Simplifying 100 + -20x + x2 + x2 + 8x + 16 = 100 Reorder the terms: 100 + 16 + -20x + 8x + x2 + x2 = 100 Combine like terms: 100 + 16 = 116 116 + -20x + 8x + x2 + x2 = 100 Combine like terms: -20x + 8x = -12x 116 + -12x + x2 + x2 = 100 Combine like terms: x2 + x2 = 2x2 116 + -12x + 2x2 = 100 Solving 116 + -12x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: 116 + -100 + -12x + 2x2 = 100 + -100 Combine like terms: 116 + -100 = 16 16 + -12x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 16 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -6x + x2) = 0 Factor a trinomial. 2((2 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {2, 4}
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