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Simplifying (-5x + -5)(9x + -1) = 25x2 + 50x + 25 Reorder the terms: (-5 + -5x)(9x + -1) = 25x2 + 50x + 25 Reorder the terms: (-5 + -5x)(-1 + 9x) = 25x2 + 50x + 25 Multiply (-5 + -5x) * (-1 + 9x) (-5(-1 + 9x) + -5x * (-1 + 9x)) = 25x2 + 50x + 25 ((-1 * -5 + 9x * -5) + -5x * (-1 + 9x)) = 25x2 + 50x + 25 ((5 + -45x) + -5x * (-1 + 9x)) = 25x2 + 50x + 25 (5 + -45x + (-1 * -5x + 9x * -5x)) = 25x2 + 50x + 25 (5 + -45x + (5x + -45x2)) = 25x2 + 50x + 25 Combine like terms: -45x + 5x = -40x (5 + -40x + -45x2) = 25x2 + 50x + 25 Reorder the terms: 5 + -40x + -45x2 = 25 + 50x + 25x2 Solving 5 + -40x + -45x2 = 25 + 50x + 25x2 Solving for variable 'x'. Reorder the terms: 5 + -25 + -40x + -50x + -45x2 + -25x2 = 25 + 50x + 25x2 + -25 + -50x + -25x2 Combine like terms: 5 + -25 = -20 -20 + -40x + -50x + -45x2 + -25x2 = 25 + 50x + 25x2 + -25 + -50x + -25x2 Combine like terms: -40x + -50x = -90x -20 + -90x + -45x2 + -25x2 = 25 + 50x + 25x2 + -25 + -50x + -25x2 Combine like terms: -45x2 + -25x2 = -70x2 -20 + -90x + -70x2 = 25 + 50x + 25x2 + -25 + -50x + -25x2 Reorder the terms: -20 + -90x + -70x2 = 25 + -25 + 50x + -50x + 25x2 + -25x2 Combine like terms: 25 + -25 = 0 -20 + -90x + -70x2 = 0 + 50x + -50x + 25x2 + -25x2 -20 + -90x + -70x2 = 50x + -50x + 25x2 + -25x2 Combine like terms: 50x + -50x = 0 -20 + -90x + -70x2 = 0 + 25x2 + -25x2 -20 + -90x + -70x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -20 + -90x + -70x2 = 0 Factor out the Greatest Common Factor (GCF), '-10'. -10(2 + 9x + 7x2) = 0 Factor a trinomial. -10((1 + x)(2 + 7x)) = 0 Ignore the factor -10.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 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 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Divide each side by '7'. x = -0.2857142857 Simplifying x = -0.2857142857Solution
x = {-1, -0.2857142857}
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