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Simplifying x(7x + 10) = 2x2 + -34x + 9 Reorder the terms: x(10 + 7x) = 2x2 + -34x + 9 (10 * x + 7x * x) = 2x2 + -34x + 9 (10x + 7x2) = 2x2 + -34x + 9 Reorder the terms: 10x + 7x2 = 9 + -34x + 2x2 Solving 10x + 7x2 = 9 + -34x + 2x2 Solving for variable 'x'. Reorder the terms: -9 + 10x + 34x + 7x2 + -2x2 = 9 + -34x + 2x2 + -9 + 34x + -2x2 Combine like terms: 10x + 34x = 44x -9 + 44x + 7x2 + -2x2 = 9 + -34x + 2x2 + -9 + 34x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 -9 + 44x + 5x2 = 9 + -34x + 2x2 + -9 + 34x + -2x2 Reorder the terms: -9 + 44x + 5x2 = 9 + -9 + -34x + 34x + 2x2 + -2x2 Combine like terms: 9 + -9 = 0 -9 + 44x + 5x2 = 0 + -34x + 34x + 2x2 + -2x2 -9 + 44x + 5x2 = -34x + 34x + 2x2 + -2x2 Combine like terms: -34x + 34x = 0 -9 + 44x + 5x2 = 0 + 2x2 + -2x2 -9 + 44x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9 + 44x + 5x2 = 0 Factor a trinomial. (-9 + -1x)(1 + -5x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {-9, 0.2}
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