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Simplifying 0 = 2x2 + 42x + -2160 Reorder the terms: 0 = -2160 + 42x + 2x2 Solving 0 = -2160 + 42x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 2160 = 2160 2160 + -42x + -2x2 = -2160 + 42x + 2x2 + 2160 + -42x + -2x2 Reorder the terms: 2160 + -42x + -2x2 = -2160 + 2160 + 42x + -42x + 2x2 + -2x2 Combine like terms: -2160 + 2160 = 0 2160 + -42x + -2x2 = 0 + 42x + -42x + 2x2 + -2x2 2160 + -42x + -2x2 = 42x + -42x + 2x2 + -2x2 Combine like terms: 42x + -42x = 0 2160 + -42x + -2x2 = 0 + 2x2 + -2x2 2160 + -42x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 2160 + -42x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1080 + -21x + -1x2) = 0 Factor a trinomial. 2((24 + -1x)(45 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Divide each side by '-1'. x = 24 Simplifying x = 24Subproblem 2
Set the factor '(45 + x)' equal to zero and attempt to solve: Simplifying 45 + x = 0 Solving 45 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + x = 0 + -45 x = 0 + -45 Combine like terms: 0 + -45 = -45 x = -45 Simplifying x = -45Solution
x = {24, -45}
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