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Simplifying 2x2 + -17x + 45 = 3x + -5 Reorder the terms: 45 + -17x + 2x2 = 3x + -5 Reorder the terms: 45 + -17x + 2x2 = -5 + 3x Solving 45 + -17x + 2x2 = -5 + 3x Solving for variable 'x'. Reorder the terms: 45 + 5 + -17x + -3x + 2x2 = -5 + 3x + 5 + -3x Combine like terms: 45 + 5 = 50 50 + -17x + -3x + 2x2 = -5 + 3x + 5 + -3x Combine like terms: -17x + -3x = -20x 50 + -20x + 2x2 = -5 + 3x + 5 + -3x Reorder the terms: 50 + -20x + 2x2 = -5 + 5 + 3x + -3x Combine like terms: -5 + 5 = 0 50 + -20x + 2x2 = 0 + 3x + -3x 50 + -20x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 50 + -20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -10x + x2) = 0 Factor a trinomial. 2((5 + -1x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {5, 5}
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