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Simplifying 0 = -16x2 + 30x + 4 Reorder the terms: 0 = 4 + 30x + -16x2 Solving 0 = 4 + 30x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -30x + 16x2 = 4 + 30x + -16x2 + -4 + -30x + 16x2 Reorder the terms: -4 + -30x + 16x2 = 4 + -4 + 30x + -30x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -30x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -4 + -30x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -4 + -30x + 16x2 = 0 + -16x2 + 16x2 -4 + -30x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -30x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -15x + 8x2) = 0 Factor a trinomial. 2((-1 + -8x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -8x)' equal to zero and attempt to solve: Simplifying -1 + -8x = 0 Solving -1 + -8x = 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 + -8x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8x = 0 + 1 -8x = 0 + 1 Combine like terms: 0 + 1 = 1 -8x = 1 Divide each side by '-8'. x = -0.125 Simplifying x = -0.125Subproblem 2
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 = 2Solution
x = {-0.125, 2}
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