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Simplifying (4x + -9)(5x + -5) = 0 Reorder the terms: (-9 + 4x)(5x + -5) = 0 Reorder the terms: (-9 + 4x)(-5 + 5x) = 0 Multiply (-9 + 4x) * (-5 + 5x) (-9(-5 + 5x) + 4x * (-5 + 5x)) = 0 ((-5 * -9 + 5x * -9) + 4x * (-5 + 5x)) = 0 ((45 + -45x) + 4x * (-5 + 5x)) = 0 (45 + -45x + (-5 * 4x + 5x * 4x)) = 0 (45 + -45x + (-20x + 20x2)) = 0 Combine like terms: -45x + -20x = -65x (45 + -65x + 20x2) = 0 Solving 45 + -65x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -13x + 4x2) = 0 Factor a trinomial. 5((1 + -1x)(9 + -4x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Solution
x = {1, 2.25}
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