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Simplifying 27x(x + 7) = 7020 Reorder the terms: 27x(7 + x) = 7020 (7 * 27x + x * 27x) = 7020 (189x + 27x2) = 7020 Solving 189x + 27x2 = 7020 Solving for variable 'x'. Reorder the terms: -7020 + 189x + 27x2 = 7020 + -7020 Combine like terms: 7020 + -7020 = 0 -7020 + 189x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '27'. 27(-260 + 7x + x2) = 0 Factor a trinomial. 27((-20 + -1x)(13 + -1x)) = 0 Ignore the factor 27.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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-20, 13}
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