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Simplifying 3x2 + -35x + 32 = -2x2 + 5x + -3 Reorder the terms: 32 + -35x + 3x2 = -2x2 + 5x + -3 Reorder the terms: 32 + -35x + 3x2 = -3 + 5x + -2x2 Solving 32 + -35x + 3x2 = -3 + 5x + -2x2 Solving for variable 'x'. Reorder the terms: 32 + 3 + -35x + -5x + 3x2 + 2x2 = -3 + 5x + -2x2 + 3 + -5x + 2x2 Combine like terms: 32 + 3 = 35 35 + -35x + -5x + 3x2 + 2x2 = -3 + 5x + -2x2 + 3 + -5x + 2x2 Combine like terms: -35x + -5x = -40x 35 + -40x + 3x2 + 2x2 = -3 + 5x + -2x2 + 3 + -5x + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 35 + -40x + 5x2 = -3 + 5x + -2x2 + 3 + -5x + 2x2 Reorder the terms: 35 + -40x + 5x2 = -3 + 3 + 5x + -5x + -2x2 + 2x2 Combine like terms: -3 + 3 = 0 35 + -40x + 5x2 = 0 + 5x + -5x + -2x2 + 2x2 35 + -40x + 5x2 = 5x + -5x + -2x2 + 2x2 Combine like terms: 5x + -5x = 0 35 + -40x + 5x2 = 0 + -2x2 + 2x2 35 + -40x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 35 + -40x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(7 + -8x + x2) = 0 Factor a trinomial. 5((1 + -1x)(7 + -1x)) = 0 Ignore the factor 5.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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