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Simplifying x2 + 10x + -5 = -3x2 + 2x Reorder the terms: -5 + 10x + x2 = -3x2 + 2x Reorder the terms: -5 + 10x + x2 = 2x + -3x2 Solving -5 + 10x + x2 = 2x + -3x2 Solving for variable 'x'. Reorder the terms: -5 + 10x + -2x + x2 + 3x2 = 2x + -3x2 + -2x + 3x2 Combine like terms: 10x + -2x = 8x -5 + 8x + x2 + 3x2 = 2x + -3x2 + -2x + 3x2 Combine like terms: x2 + 3x2 = 4x2 -5 + 8x + 4x2 = 2x + -3x2 + -2x + 3x2 Reorder the terms: -5 + 8x + 4x2 = 2x + -2x + -3x2 + 3x2 Combine like terms: 2x + -2x = 0 -5 + 8x + 4x2 = 0 + -3x2 + 3x2 -5 + 8x + 4x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -5 + 8x + 4x2 = 0 Factor a trinomial. (-5 + -2x)(1 + -2x) = 0Subproblem 1
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 = -2.5Subproblem 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 = {-2.5, 0.5}
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