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Simplifying x(5x + 3) = 2x2 + -8x + 4 Reorder the terms: x(3 + 5x) = 2x2 + -8x + 4 (3 * x + 5x * x) = 2x2 + -8x + 4 (3x + 5x2) = 2x2 + -8x + 4 Reorder the terms: 3x + 5x2 = 4 + -8x + 2x2 Solving 3x + 5x2 = 4 + -8x + 2x2 Solving for variable 'x'. Reorder the terms: -4 + 3x + 8x + 5x2 + -2x2 = 4 + -8x + 2x2 + -4 + 8x + -2x2 Combine like terms: 3x + 8x = 11x -4 + 11x + 5x2 + -2x2 = 4 + -8x + 2x2 + -4 + 8x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -4 + 11x + 3x2 = 4 + -8x + 2x2 + -4 + 8x + -2x2 Reorder the terms: -4 + 11x + 3x2 = 4 + -4 + -8x + 8x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 -4 + 11x + 3x2 = 0 + -8x + 8x + 2x2 + -2x2 -4 + 11x + 3x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 -4 + 11x + 3x2 = 0 + 2x2 + -2x2 -4 + 11x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + 11x + 3x2 = 0 Factor a trinomial. (-4 + -1x)(1 + -3x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 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 = {-4, 0.3333333333}
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