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Simplifying 10 + -5x + -2x2 = 2x2 + 3x + 5 Reorder the terms: 10 + -5x + -2x2 = 5 + 3x + 2x2 Solving 10 + -5x + -2x2 = 5 + 3x + 2x2 Solving for variable 'x'. Reorder the terms: 10 + -5 + -5x + -3x + -2x2 + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2 Combine like terms: 10 + -5 = 5 5 + -5x + -3x + -2x2 + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2 Combine like terms: -5x + -3x = -8x 5 + -8x + -2x2 + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2 Combine like terms: -2x2 + -2x2 = -4x2 5 + -8x + -4x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2 Reorder the terms: 5 + -8x + -4x2 = 5 + -5 + 3x + -3x + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 5 + -8x + -4x2 = 0 + 3x + -3x + 2x2 + -2x2 5 + -8x + -4x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 5 + -8x + -4x2 = 0 + 2x2 + -2x2 5 + -8x + -4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + -8x + -4x2 = 0 Factor a trinomial. (1 + -2x)(5 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {0.5, -2.5}
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