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Simplifying 0 = -4x2 + 32x + -28 Reorder the terms: 0 = -28 + 32x + -4x2 Solving 0 = -28 + 32x + -4x2 Solving for variable 'x'. Combine like terms: 0 + 28 = 28 28 + -32x + 4x2 = -28 + 32x + -4x2 + 28 + -32x + 4x2 Reorder the terms: 28 + -32x + 4x2 = -28 + 28 + 32x + -32x + -4x2 + 4x2 Combine like terms: -28 + 28 = 0 28 + -32x + 4x2 = 0 + 32x + -32x + -4x2 + 4x2 28 + -32x + 4x2 = 32x + -32x + -4x2 + 4x2 Combine like terms: 32x + -32x = 0 28 + -32x + 4x2 = 0 + -4x2 + 4x2 28 + -32x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 28 + -32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -8x + x2) = 0 Factor a trinomial. 4((1 + -1x)(7 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1, 7}
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