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Simplifying -16x2 + 22x + 100 = 80 Reorder the terms: 100 + 22x + -16x2 = 80 Solving 100 + 22x + -16x2 = 80 Solving for variable 'x'. Reorder the terms: 100 + -80 + 22x + -16x2 = 80 + -80 Combine like terms: 100 + -80 = 20 20 + 22x + -16x2 = 80 + -80 Combine like terms: 80 + -80 = 0 20 + 22x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 11x + -8x2) = 0 Factor a trinomial. 2((2 + -1x)(5 + 8x)) = 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 '(5 + 8x)' equal to zero and attempt to solve: Simplifying 5 + 8x = 0 Solving 5 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8x = 0 + -5 8x = 0 + -5 Combine like terms: 0 + -5 = -5 8x = -5 Divide each side by '8'. x = -0.625 Simplifying x = -0.625Solution
x = {2, -0.625}
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