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Simplifying x(5x + 7) = 2x2 + -7x + 5 Reorder the terms: x(7 + 5x) = 2x2 + -7x + 5 (7 * x + 5x * x) = 2x2 + -7x + 5 (7x + 5x2) = 2x2 + -7x + 5 Reorder the terms: 7x + 5x2 = 5 + -7x + 2x2 Solving 7x + 5x2 = 5 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -5 + 7x + 7x + 5x2 + -2x2 = 5 + -7x + 2x2 + -5 + 7x + -2x2 Combine like terms: 7x + 7x = 14x -5 + 14x + 5x2 + -2x2 = 5 + -7x + 2x2 + -5 + 7x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -5 + 14x + 3x2 = 5 + -7x + 2x2 + -5 + 7x + -2x2 Reorder the terms: -5 + 14x + 3x2 = 5 + -5 + -7x + 7x + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 -5 + 14x + 3x2 = 0 + -7x + 7x + 2x2 + -2x2 -5 + 14x + 3x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 -5 + 14x + 3x2 = 0 + 2x2 + -2x2 -5 + 14x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 14x + 3x2 = 0 Factor a trinomial. (-5 + -1x)(1 + -3x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-5, 0.3333333333}
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