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Simplifying 3x2 + -17x + 33 = x2 + -8x + 38 Reorder the terms: 33 + -17x + 3x2 = x2 + -8x + 38 Reorder the terms: 33 + -17x + 3x2 = 38 + -8x + x2 Solving 33 + -17x + 3x2 = 38 + -8x + x2 Solving for variable 'x'. Reorder the terms: 33 + -38 + -17x + 8x + 3x2 + -1x2 = 38 + -8x + x2 + -38 + 8x + -1x2 Combine like terms: 33 + -38 = -5 -5 + -17x + 8x + 3x2 + -1x2 = 38 + -8x + x2 + -38 + 8x + -1x2 Combine like terms: -17x + 8x = -9x -5 + -9x + 3x2 + -1x2 = 38 + -8x + x2 + -38 + 8x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -5 + -9x + 2x2 = 38 + -8x + x2 + -38 + 8x + -1x2 Reorder the terms: -5 + -9x + 2x2 = 38 + -38 + -8x + 8x + x2 + -1x2 Combine like terms: 38 + -38 = 0 -5 + -9x + 2x2 = 0 + -8x + 8x + x2 + -1x2 -5 + -9x + 2x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 -5 + -9x + 2x2 = 0 + x2 + -1x2 -5 + -9x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5 + -9x + 2x2 = 0 Factor a trinomial. (-1 + -2x)(5 + -1x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
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 = 5Solution
x = {-0.5, 5}
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