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Simplifying 0 = 2x2 + -110x + 500 Reorder the terms: 0 = 500 + -110x + 2x2 Solving 0 = 500 + -110x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -500 = -500 -500 + 110x + -2x2 = 500 + -110x + 2x2 + -500 + 110x + -2x2 Reorder the terms: -500 + 110x + -2x2 = 500 + -500 + -110x + 110x + 2x2 + -2x2 Combine like terms: 500 + -500 = 0 -500 + 110x + -2x2 = 0 + -110x + 110x + 2x2 + -2x2 -500 + 110x + -2x2 = -110x + 110x + 2x2 + -2x2 Combine like terms: -110x + 110x = 0 -500 + 110x + -2x2 = 0 + 2x2 + -2x2 -500 + 110x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -500 + 110x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + 55x + -1x2) = 0 Factor a trinomial. 2((-50 + x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + x)' equal to zero and attempt to solve: Simplifying -50 + x = 0 Solving -50 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x = 0 + 50 x = 0 + 50 Combine like terms: 0 + 50 = 50 x = 50 Simplifying x = 50Subproblem 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 = {50, 5}
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