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Simplifying 6x2 + -17x + 13 = 20x2 + -32 Reorder the terms: 13 + -17x + 6x2 = 20x2 + -32 Reorder the terms: 13 + -17x + 6x2 = -32 + 20x2 Solving 13 + -17x + 6x2 = -32 + 20x2 Solving for variable 'x'. Reorder the terms: 13 + 32 + -17x + 6x2 + -20x2 = -32 + 20x2 + 32 + -20x2 Combine like terms: 13 + 32 = 45 45 + -17x + 6x2 + -20x2 = -32 + 20x2 + 32 + -20x2 Combine like terms: 6x2 + -20x2 = -14x2 45 + -17x + -14x2 = -32 + 20x2 + 32 + -20x2 Reorder the terms: 45 + -17x + -14x2 = -32 + 32 + 20x2 + -20x2 Combine like terms: -32 + 32 = 0 45 + -17x + -14x2 = 0 + 20x2 + -20x2 45 + -17x + -14x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 45 + -17x + -14x2 = 0 Factor a trinomial. (9 + -7x)(5 + 2x) = 0Subproblem 1
Set the factor '(9 + -7x)' equal to zero and attempt to solve: Simplifying 9 + -7x = 0 Solving 9 + -7x = 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 + -7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x = 0 + -9 -7x = 0 + -9 Combine like terms: 0 + -9 = -9 -7x = -9 Divide each side by '-7'. x = 1.285714286 Simplifying x = 1.285714286Subproblem 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 = {1.285714286, -2.5}
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