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Simplifying 3x2 + 5x = x + -1 + -1x2 Reorder the terms: 5x + 3x2 = x + -1 + -1x2 Reorder the terms: 5x + 3x2 = -1 + x + -1x2 Solving 5x + 3x2 = -1 + x + -1x2 Solving for variable 'x'. Reorder the terms: 1 + 5x + -1x + 3x2 + x2 = -1 + x + -1x2 + 1 + -1x + x2 Combine like terms: 5x + -1x = 4x 1 + 4x + 3x2 + x2 = -1 + x + -1x2 + 1 + -1x + x2 Combine like terms: 3x2 + x2 = 4x2 1 + 4x + 4x2 = -1 + x + -1x2 + 1 + -1x + x2 Reorder the terms: 1 + 4x + 4x2 = -1 + 1 + x + -1x + -1x2 + x2 Combine like terms: -1 + 1 = 0 1 + 4x + 4x2 = 0 + x + -1x + -1x2 + x2 1 + 4x + 4x2 = x + -1x + -1x2 + x2 Combine like terms: x + -1x = 0 1 + 4x + 4x2 = 0 + -1x2 + x2 1 + 4x + 4x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1 + 4x + 4x2 = 0 Factor a trinomial. (1 + 2x)(1 + 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 '(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 = -0.5Solution
x = {-0.5, -0.5}
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