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Simplifying 32x2 + -3x + -14 = 4x2 + -4x + 1 Reorder the terms: -14 + -3x + 32x2 = 4x2 + -4x + 1 Reorder the terms: -14 + -3x + 32x2 = 1 + -4x + 4x2 Solving -14 + -3x + 32x2 = 1 + -4x + 4x2 Solving for variable 'x'. Reorder the terms: -14 + -1 + -3x + 4x + 32x2 + -4x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2 Combine like terms: -14 + -1 = -15 -15 + -3x + 4x + 32x2 + -4x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2 Combine like terms: -3x + 4x = 1x -15 + 1x + 32x2 + -4x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2 Combine like terms: 32x2 + -4x2 = 28x2 -15 + 1x + 28x2 = 1 + -4x + 4x2 + -1 + 4x + -4x2 Reorder the terms: -15 + 1x + 28x2 = 1 + -1 + -4x + 4x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 -15 + 1x + 28x2 = 0 + -4x + 4x + 4x2 + -4x2 -15 + 1x + 28x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 -15 + 1x + 28x2 = 0 + 4x2 + -4x2 -15 + 1x + 28x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + 1x + 28x2 = 0 Factor a trinomial. (-3 + -4x)(5 + -7x) = 0Subproblem 1
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 = -0.75Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Solution
x = {-0.75, 0.7142857143}
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