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Simplifying 24 = -0.5 * 32x2 + 32x + 12 Multiply -0.5 * 32 24 = -16x2 + 32x + 12 Reorder the terms: 24 = 12 + 32x + -16x2 Solving 24 = 12 + 32x + -16x2 Solving for variable 'x'. Combine like terms: 24 + -12 = 12 12 + -32x + 16x2 = 12 + 32x + -16x2 + -12 + -32x + 16x2 Reorder the terms: 12 + -32x + 16x2 = 12 + -12 + 32x + -32x + -16x2 + 16x2 Combine like terms: 12 + -12 = 0 12 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 12 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 12 + -32x + 16x2 = 0 + -16x2 + 16x2 12 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 12 + -32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -8x + 4x2) = 0 Factor a trinomial. 4((1 + -2x)(3 + -2x)) = 0 Ignore the factor 4.Subproblem 1
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 = 0.5Subproblem 2
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 = 1.5Solution
x = {0.5, 1.5}
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