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Simplifying 0.5((x + 3) + (7x + -9))(3x + -1) = 72 Reorder the terms: 0.5((3 + x) + (7x + -9))(3x + -1) = 72 Remove parenthesis around (3 + x) 0.5(3 + x + (7x + -9))(3x + -1) = 72 Reorder the terms: 0.5(3 + x + (-9 + 7x))(3x + -1) = 72 Remove parenthesis around (-9 + 7x) 0.5(3 + x + -9 + 7x)(3x + -1) = 72 Reorder the terms: 0.5(3 + -9 + x + 7x)(3x + -1) = 72 Combine like terms: 3 + -9 = -6 0.5(-6 + x + 7x)(3x + -1) = 72 Combine like terms: x + 7x = 8x 0.5(-6 + 8x)(3x + -1) = 72 Reorder the terms: 0.5(-6 + 8x)(-1 + 3x) = 72 Multiply (-6 + 8x) * (-1 + 3x) 0.5(-6(-1 + 3x) + 8x * (-1 + 3x)) = 72 0.5((-1 * -6 + 3x * -6) + 8x * (-1 + 3x)) = 72 0.5((6 + -18x) + 8x * (-1 + 3x)) = 72 0.5(6 + -18x + (-1 * 8x + 3x * 8x)) = 72 0.5(6 + -18x + (-8x + 24x2)) = 72 Combine like terms: -18x + -8x = -26x 0.5(6 + -26x + 24x2) = 72 (6 * 0.5 + -26x * 0.5 + 24x2 * 0.5) = 72 (3 + -13x + 12x2) = 72 Solving 3 + -13x + 12x2 = 72 Solving for variable 'x'. Reorder the terms: 3 + -72 + -13x + 12x2 = 72 + -72 Combine like terms: 3 + -72 = -69 -69 + -13x + 12x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -69 + -13x + 12x2 = 0 Factor a trinomial. (-23 + -12x)(3 + -1x) = 0Subproblem 1
Set the factor '(-23 + -12x)' equal to zero and attempt to solve: Simplifying -23 + -12x = 0 Solving -23 + -12x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -12x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -12x = 0 + 23 -12x = 0 + 23 Combine like terms: 0 + 23 = 23 -12x = 23 Divide each side by '-12'. x = -1.916666667 Simplifying x = -1.916666667Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1.916666667, 3}
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