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Simplifying -8X2 + 58X + -145 = -5X2 + 31X + -85 Reorder the terms: -145 + 58X + -8X2 = -5X2 + 31X + -85 Reorder the terms: -145 + 58X + -8X2 = -85 + 31X + -5X2 Solving -145 + 58X + -8X2 = -85 + 31X + -5X2 Solving for variable 'X'. Reorder the terms: -145 + 85 + 58X + -31X + -8X2 + 5X2 = -85 + 31X + -5X2 + 85 + -31X + 5X2 Combine like terms: -145 + 85 = -60 -60 + 58X + -31X + -8X2 + 5X2 = -85 + 31X + -5X2 + 85 + -31X + 5X2 Combine like terms: 58X + -31X = 27X -60 + 27X + -8X2 + 5X2 = -85 + 31X + -5X2 + 85 + -31X + 5X2 Combine like terms: -8X2 + 5X2 = -3X2 -60 + 27X + -3X2 = -85 + 31X + -5X2 + 85 + -31X + 5X2 Reorder the terms: -60 + 27X + -3X2 = -85 + 85 + 31X + -31X + -5X2 + 5X2 Combine like terms: -85 + 85 = 0 -60 + 27X + -3X2 = 0 + 31X + -31X + -5X2 + 5X2 -60 + 27X + -3X2 = 31X + -31X + -5X2 + 5X2 Combine like terms: 31X + -31X = 0 -60 + 27X + -3X2 = 0 + -5X2 + 5X2 -60 + 27X + -3X2 = -5X2 + 5X2 Combine like terms: -5X2 + 5X2 = 0 -60 + 27X + -3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + 9X + -1X2) = 0 Factor a trinomial. 3((-5 + X)(4 + -1X)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + X)' equal to zero and attempt to solve: Simplifying -5 + X = 0 Solving -5 + X = 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 + X = 0 + 5 Combine like terms: -5 + 5 = 0 0 + X = 0 + 5 X = 0 + 5 Combine like terms: 0 + 5 = 5 X = 5 Simplifying X = 5Subproblem 2
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 = 4Solution
X = {5, 4}
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