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Simplifying 410 = -16x2 + 4x + 412 Reorder the terms: 410 = 412 + 4x + -16x2 Solving 410 = 412 + 4x + -16x2 Solving for variable 'x'. Combine like terms: 410 + -412 = -2 -2 + -4x + 16x2 = 412 + 4x + -16x2 + -412 + -4x + 16x2 Reorder the terms: -2 + -4x + 16x2 = 412 + -412 + 4x + -4x + -16x2 + 16x2 Combine like terms: 412 + -412 = 0 -2 + -4x + 16x2 = 0 + 4x + -4x + -16x2 + 16x2 -2 + -4x + 16x2 = 4x + -4x + -16x2 + 16x2 Combine like terms: 4x + -4x = 0 -2 + -4x + 16x2 = 0 + -16x2 + 16x2 -2 + -4x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2 + -4x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2x + 8x2) = 0 Factor a trinomial. 2((-1 + -4x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.25Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-0.25, 0.5}
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