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Simplifying 5X2 + -47X + 70 = 3X2 + -31X + 46 Reorder the terms: 70 + -47X + 5X2 = 3X2 + -31X + 46 Reorder the terms: 70 + -47X + 5X2 = 46 + -31X + 3X2 Solving 70 + -47X + 5X2 = 46 + -31X + 3X2 Solving for variable 'X'. Reorder the terms: 70 + -46 + -47X + 31X + 5X2 + -3X2 = 46 + -31X + 3X2 + -46 + 31X + -3X2 Combine like terms: 70 + -46 = 24 24 + -47X + 31X + 5X2 + -3X2 = 46 + -31X + 3X2 + -46 + 31X + -3X2 Combine like terms: -47X + 31X = -16X 24 + -16X + 5X2 + -3X2 = 46 + -31X + 3X2 + -46 + 31X + -3X2 Combine like terms: 5X2 + -3X2 = 2X2 24 + -16X + 2X2 = 46 + -31X + 3X2 + -46 + 31X + -3X2 Reorder the terms: 24 + -16X + 2X2 = 46 + -46 + -31X + 31X + 3X2 + -3X2 Combine like terms: 46 + -46 = 0 24 + -16X + 2X2 = 0 + -31X + 31X + 3X2 + -3X2 24 + -16X + 2X2 = -31X + 31X + 3X2 + -3X2 Combine like terms: -31X + 31X = 0 24 + -16X + 2X2 = 0 + 3X2 + -3X2 24 + -16X + 2X2 = 3X2 + -3X2 Combine like terms: 3X2 + -3X2 = 0 24 + -16X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -8X + X2) = 0 Factor a trinomial. 2((2 + -1X)(6 + -1X)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1X)' equal to zero and attempt to solve: Simplifying 2 + -1X = 0 Solving 2 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1X = 0 + -2 -1X = 0 + -2 Combine like terms: 0 + -2 = -2 -1X = -2 Divide each side by '-1'. X = 2 Simplifying X = 2Subproblem 2
Set the factor '(6 + -1X)' equal to zero and attempt to solve: Simplifying 6 + -1X = 0 Solving 6 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1X = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1X = 0 + -6 -1X = 0 + -6 Combine like terms: 0 + -6 = -6 -1X = -6 Divide each side by '-1'. X = 6 Simplifying X = 6Solution
X = {2, 6}
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