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Simplifying 8x2 + -89x + 173 = 5x2 + -56x + 89 Reorder the terms: 173 + -89x + 8x2 = 5x2 + -56x + 89 Reorder the terms: 173 + -89x + 8x2 = 89 + -56x + 5x2 Solving 173 + -89x + 8x2 = 89 + -56x + 5x2 Solving for variable 'x'. Reorder the terms: 173 + -89 + -89x + 56x + 8x2 + -5x2 = 89 + -56x + 5x2 + -89 + 56x + -5x2 Combine like terms: 173 + -89 = 84 84 + -89x + 56x + 8x2 + -5x2 = 89 + -56x + 5x2 + -89 + 56x + -5x2 Combine like terms: -89x + 56x = -33x 84 + -33x + 8x2 + -5x2 = 89 + -56x + 5x2 + -89 + 56x + -5x2 Combine like terms: 8x2 + -5x2 = 3x2 84 + -33x + 3x2 = 89 + -56x + 5x2 + -89 + 56x + -5x2 Reorder the terms: 84 + -33x + 3x2 = 89 + -89 + -56x + 56x + 5x2 + -5x2 Combine like terms: 89 + -89 = 0 84 + -33x + 3x2 = 0 + -56x + 56x + 5x2 + -5x2 84 + -33x + 3x2 = -56x + 56x + 5x2 + -5x2 Combine like terms: -56x + 56x = 0 84 + -33x + 3x2 = 0 + 5x2 + -5x2 84 + -33x + 3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 84 + -33x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(28 + -11x + x2) = 0 Factor a trinomial. 3((4 + -1x)(7 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 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 = {4, 7}
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