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Simplifying (2x + -5)(9x + -7) + (2x + -5)(x + -3) = 0 Reorder the terms: (-5 + 2x)(9x + -7) + (2x + -5)(x + -3) = 0 Reorder the terms: (-5 + 2x)(-7 + 9x) + (2x + -5)(x + -3) = 0 Multiply (-5 + 2x) * (-7 + 9x) (-5(-7 + 9x) + 2x * (-7 + 9x)) + (2x + -5)(x + -3) = 0 ((-7 * -5 + 9x * -5) + 2x * (-7 + 9x)) + (2x + -5)(x + -3) = 0 ((35 + -45x) + 2x * (-7 + 9x)) + (2x + -5)(x + -3) = 0 (35 + -45x + (-7 * 2x + 9x * 2x)) + (2x + -5)(x + -3) = 0 (35 + -45x + (-14x + 18x2)) + (2x + -5)(x + -3) = 0 Combine like terms: -45x + -14x = -59x (35 + -59x + 18x2) + (2x + -5)(x + -3) = 0 Reorder the terms: 35 + -59x + 18x2 + (-5 + 2x)(x + -3) = 0 Reorder the terms: 35 + -59x + 18x2 + (-5 + 2x)(-3 + x) = 0 Multiply (-5 + 2x) * (-3 + x) 35 + -59x + 18x2 + (-5(-3 + x) + 2x * (-3 + x)) = 0 35 + -59x + 18x2 + ((-3 * -5 + x * -5) + 2x * (-3 + x)) = 0 35 + -59x + 18x2 + ((15 + -5x) + 2x * (-3 + x)) = 0 35 + -59x + 18x2 + (15 + -5x + (-3 * 2x + x * 2x)) = 0 35 + -59x + 18x2 + (15 + -5x + (-6x + 2x2)) = 0 Combine like terms: -5x + -6x = -11x 35 + -59x + 18x2 + (15 + -11x + 2x2) = 0 Reorder the terms: 35 + 15 + -59x + -11x + 18x2 + 2x2 = 0 Combine like terms: 35 + 15 = 50 50 + -59x + -11x + 18x2 + 2x2 = 0 Combine like terms: -59x + -11x = -70x 50 + -70x + 18x2 + 2x2 = 0 Combine like terms: 18x2 + 2x2 = 20x2 50 + -70x + 20x2 = 0 Solving 50 + -70x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(5 + -7x + 2x2) = 0 Factor a trinomial. 10((1 + -1x)(5 + -2x)) = 0 Ignore the factor 10.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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {1, 2.5}
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