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