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