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Simplifying 0 = 2x2 + -106x + 480 Reorder the terms: 0 = 480 + -106x + 2x2 Solving 0 = 480 + -106x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -480 = -480 -480 + 106x + -2x2 = 480 + -106x + 2x2 + -480 + 106x + -2x2 Reorder the terms: -480 + 106x + -2x2 = 480 + -480 + -106x + 106x + 2x2 + -2x2 Combine like terms: 480 + -480 = 0 -480 + 106x + -2x2 = 0 + -106x + 106x + 2x2 + -2x2 -480 + 106x + -2x2 = -106x + 106x + 2x2 + -2x2 Combine like terms: -106x + 106x = 0 -480 + 106x + -2x2 = 0 + 2x2 + -2x2 -480 + 106x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -480 + 106x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-240 + 53x + -1x2) = 0 Factor a trinomial. 2((-48 + x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + x)' equal to zero and attempt to solve: Simplifying -48 + x = 0 Solving -48 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 0 + 48 Combine like terms: -48 + 48 = 0 0 + x = 0 + 48 x = 0 + 48 Combine like terms: 0 + 48 = 48 x = 48 Simplifying x = 48Subproblem 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 = {48, 5}
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