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Simplifying x(9x + 45) = 450 Reorder the terms: x(45 + 9x) = 450 (45 * x + 9x * x) = 450 (45x + 9x2) = 450 Solving 45x + 9x2 = 450 Solving for variable 'x'. Reorder the terms: -450 + 45x + 9x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + 45x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-50 + 5x + x2) = 0 Factor a trinomial. 9((-10 + -1x)(5 + -1x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 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 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 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 = {-10, 5}
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