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Simplifying 16x2 + -76x + 78 = 0 Reorder the terms: 78 + -76x + 16x2 = 0 Solving 78 + -76x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(39 + -38x + 8x2) = 0 Factor a trinomial. 2((3 + -2x)(13 + -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 '(13 + -4x)' equal to zero and attempt to solve: Simplifying 13 + -4x = 0 Solving 13 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -4x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -4x = 0 + -13 -4x = 0 + -13 Combine like terms: 0 + -13 = -13 -4x = -13 Divide each side by '-4'. x = 3.25 Simplifying x = 3.25Solution
x = {1.5, 3.25}
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