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Simplifying x(x + 1) = 2 + -5x2 Reorder the terms: x(1 + x) = 2 + -5x2 (1 * x + x * x) = 2 + -5x2 (1x + x2) = 2 + -5x2 Solving 1x + x2 = 2 + -5x2 Solving for variable 'x'. Reorder the terms: -2 + 1x + x2 + 5x2 = 2 + -5x2 + -2 + 5x2 Combine like terms: x2 + 5x2 = 6x2 -2 + 1x + 6x2 = 2 + -5x2 + -2 + 5x2 Reorder the terms: -2 + 1x + 6x2 = 2 + -2 + -5x2 + 5x2 Combine like terms: 2 + -2 = 0 -2 + 1x + 6x2 = 0 + -5x2 + 5x2 -2 + 1x + 6x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -2 + 1x + 6x2 = 0 Factor a trinomial. (-2 + -3x)(1 + -2x) = 0Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 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 = {-0.6666666667, 0.5}
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