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Simplifying 4x2 + 3(4x2 + -32x + 64) = 52 Reorder the terms: 4x2 + 3(64 + -32x + 4x2) = 52 4x2 + (64 * 3 + -32x * 3 + 4x2 * 3) = 52 4x2 + (192 + -96x + 12x2) = 52 Reorder the terms: 192 + -96x + 4x2 + 12x2 = 52 Combine like terms: 4x2 + 12x2 = 16x2 192 + -96x + 16x2 = 52 Solving 192 + -96x + 16x2 = 52 Solving for variable 'x'. Reorder the terms: 192 + -52 + -96x + 16x2 = 52 + -52 Combine like terms: 192 + -52 = 140 140 + -96x + 16x2 = 52 + -52 Combine like terms: 52 + -52 = 0 140 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -24x + 4x2) = 0 Factor a trinomial. 4((5 + -2x)(7 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {2.5, 3.5}
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