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Simplifying 0 = 12x2 + -77x + -20 Reorder the terms: 0 = -20 + -77x + 12x2 Solving 0 = -20 + -77x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + 77x + -12x2 = -20 + -77x + 12x2 + 20 + 77x + -12x2 Reorder the terms: 20 + 77x + -12x2 = -20 + 20 + -77x + 77x + 12x2 + -12x2 Combine like terms: -20 + 20 = 0 20 + 77x + -12x2 = 0 + -77x + 77x + 12x2 + -12x2 20 + 77x + -12x2 = -77x + 77x + 12x2 + -12x2 Combine like terms: -77x + 77x = 0 20 + 77x + -12x2 = 0 + 12x2 + -12x2 20 + 77x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 20 + 77x + -12x2 = 0 Factor a trinomial. (20 + -3x)(1 + 4x) = 0Subproblem 1
Set the factor '(20 + -3x)' equal to zero and attempt to solve: Simplifying 20 + -3x = 0 Solving 20 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -3x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -3x = 0 + -20 -3x = 0 + -20 Combine like terms: 0 + -20 = -20 -3x = -20 Divide each side by '-3'. x = 6.666666667 Simplifying x = 6.666666667Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {6.666666667, -0.25}
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