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Simplifying -16x2 + 68x + 4 = 20 Reorder the terms: 4 + 68x + -16x2 = 20 Solving 4 + 68x + -16x2 = 20 Solving for variable 'x'. Reorder the terms: 4 + -20 + 68x + -16x2 = 20 + -20 Combine like terms: 4 + -20 = -16 -16 + 68x + -16x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -16 + 68x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 17x + -4x2) = 0 Factor a trinomial. 4((-4 + x)(1 + -4x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {4, 0.25}
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