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Simplifying (4x + -3) + -16x2 = 9 + -24x Reorder the terms: (-3 + 4x) + -16x2 = 9 + -24x Remove parenthesis around (-3 + 4x) -3 + 4x + -16x2 = 9 + -24x Solving -3 + 4x + -16x2 = 9 + -24x Solving for variable 'x'. Reorder the terms: -3 + -9 + 4x + 24x + -16x2 = 9 + -24x + -9 + 24x Combine like terms: -3 + -9 = -12 -12 + 4x + 24x + -16x2 = 9 + -24x + -9 + 24x Combine like terms: 4x + 24x = 28x -12 + 28x + -16x2 = 9 + -24x + -9 + 24x Reorder the terms: -12 + 28x + -16x2 = 9 + -9 + -24x + 24x Combine like terms: 9 + -9 = 0 -12 + 28x + -16x2 = 0 + -24x + 24x -12 + 28x + -16x2 = -24x + 24x Combine like terms: -24x + 24x = 0 -12 + 28x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 7x + -4x2) = 0 Factor a trinomial. 4((-1 + x)(3 + -4x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {1, 0.75}
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