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Simplifying (9x)(27x + 11) = (17x + 5)(14x + 6) Remove parenthesis around (9x) 9x(27x + 11) = (17x + 5)(14x + 6) Reorder the terms: 9x(11 + 27x) = (17x + 5)(14x + 6) (11 * 9x + 27x * 9x) = (17x + 5)(14x + 6) (99x + 243x2) = (17x + 5)(14x + 6) Reorder the terms: 99x + 243x2 = (5 + 17x)(14x + 6) Reorder the terms: 99x + 243x2 = (5 + 17x)(6 + 14x) Multiply (5 + 17x) * (6 + 14x) 99x + 243x2 = (5(6 + 14x) + 17x * (6 + 14x)) 99x + 243x2 = ((6 * 5 + 14x * 5) + 17x * (6 + 14x)) 99x + 243x2 = ((30 + 70x) + 17x * (6 + 14x)) 99x + 243x2 = (30 + 70x + (6 * 17x + 14x * 17x)) 99x + 243x2 = (30 + 70x + (102x + 238x2)) Combine like terms: 70x + 102x = 172x 99x + 243x2 = (30 + 172x + 238x2) Solving 99x + 243x2 = 30 + 172x + 238x2 Solving for variable 'x'. Reorder the terms: -30 + 99x + -172x + 243x2 + -238x2 = 30 + 172x + 238x2 + -30 + -172x + -238x2 Combine like terms: 99x + -172x = -73x -30 + -73x + 243x2 + -238x2 = 30 + 172x + 238x2 + -30 + -172x + -238x2 Combine like terms: 243x2 + -238x2 = 5x2 -30 + -73x + 5x2 = 30 + 172x + 238x2 + -30 + -172x + -238x2 Reorder the terms: -30 + -73x + 5x2 = 30 + -30 + 172x + -172x + 238x2 + -238x2 Combine like terms: 30 + -30 = 0 -30 + -73x + 5x2 = 0 + 172x + -172x + 238x2 + -238x2 -30 + -73x + 5x2 = 172x + -172x + 238x2 + -238x2 Combine like terms: 172x + -172x = 0 -30 + -73x + 5x2 = 0 + 238x2 + -238x2 -30 + -73x + 5x2 = 238x2 + -238x2 Combine like terms: 238x2 + -238x2 = 0 -30 + -73x + 5x2 = 0 Factor a trinomial. (-2 + -5x)(15 + -1x) = 0Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-0.4, 15}
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