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Simplifying 164 = -16x2 + 100x + 50 Reorder the terms: 164 = 50 + 100x + -16x2 Solving 164 = 50 + 100x + -16x2 Solving for variable 'x'. Combine like terms: 164 + -50 = 114 114 + -100x + 16x2 = 50 + 100x + -16x2 + -50 + -100x + 16x2 Reorder the terms: 114 + -100x + 16x2 = 50 + -50 + 100x + -100x + -16x2 + 16x2 Combine like terms: 50 + -50 = 0 114 + -100x + 16x2 = 0 + 100x + -100x + -16x2 + 16x2 114 + -100x + 16x2 = 100x + -100x + -16x2 + 16x2 Combine like terms: 100x + -100x = 0 114 + -100x + 16x2 = 0 + -16x2 + 16x2 114 + -100x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 114 + -100x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(57 + -50x + 8x2) = 0 Factor a trinomial. 2((3 + -2x)(19 + -4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(19 + -4x)' equal to zero and attempt to solve: Simplifying 19 + -4x = 0 Solving 19 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -4x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -4x = 0 + -19 -4x = 0 + -19 Combine like terms: 0 + -19 = -19 -4x = -19 Divide each side by '-4'. x = 4.75 Simplifying x = 4.75Solution
x = {1.5, 4.75}
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