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Simplifying 450 = 3x2 + -30x + -150 Reorder the terms: 450 = -150 + -30x + 3x2 Solving 450 = -150 + -30x + 3x2 Solving for variable 'x'. Combine like terms: 450 + 150 = 600 600 + 30x + -3x2 = -150 + -30x + 3x2 + 150 + 30x + -3x2 Reorder the terms: 600 + 30x + -3x2 = -150 + 150 + -30x + 30x + 3x2 + -3x2 Combine like terms: -150 + 150 = 0 600 + 30x + -3x2 = 0 + -30x + 30x + 3x2 + -3x2 600 + 30x + -3x2 = -30x + 30x + 3x2 + -3x2 Combine like terms: -30x + 30x = 0 600 + 30x + -3x2 = 0 + 3x2 + -3x2 600 + 30x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 600 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(200 + 10x + -1x2) = 0 Factor a trinomial. 3((20 + -1x)(10 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {20, -10}
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