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Simplifying 3x2 + -5x = x2 + -2x + 9 Reorder the terms: -5x + 3x2 = x2 + -2x + 9 Reorder the terms: -5x + 3x2 = 9 + -2x + x2 Solving -5x + 3x2 = 9 + -2x + x2 Solving for variable 'x'. Reorder the terms: -9 + -5x + 2x + 3x2 + -1x2 = 9 + -2x + x2 + -9 + 2x + -1x2 Combine like terms: -5x + 2x = -3x -9 + -3x + 3x2 + -1x2 = 9 + -2x + x2 + -9 + 2x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -9 + -3x + 2x2 = 9 + -2x + x2 + -9 + 2x + -1x2 Reorder the terms: -9 + -3x + 2x2 = 9 + -9 + -2x + 2x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -9 + -3x + 2x2 = 0 + -2x + 2x + x2 + -1x2 -9 + -3x + 2x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -9 + -3x + 2x2 = 0 + x2 + -1x2 -9 + -3x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + -3x + 2x2 = 0 Factor a trinomial. (-3 + -2x)(3 + -1x) = 0Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
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 = 3Solution
x = {-1.5, 3}
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