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Simplifying 6x2 + 5x = 5 + -2x2 + -1x Reorder the terms: 5x + 6x2 = 5 + -2x2 + -1x Reorder the terms: 5x + 6x2 = 5 + -1x + -2x2 Solving 5x + 6x2 = 5 + -1x + -2x2 Solving for variable 'x'. Reorder the terms: -5 + 5x + x + 6x2 + 2x2 = 5 + -1x + -2x2 + -5 + x + 2x2 Combine like terms: 5x + x = 6x -5 + 6x + 6x2 + 2x2 = 5 + -1x + -2x2 + -5 + x + 2x2 Combine like terms: 6x2 + 2x2 = 8x2 -5 + 6x + 8x2 = 5 + -1x + -2x2 + -5 + x + 2x2 Reorder the terms: -5 + 6x + 8x2 = 5 + -5 + -1x + x + -2x2 + 2x2 Combine like terms: 5 + -5 = 0 -5 + 6x + 8x2 = 0 + -1x + x + -2x2 + 2x2 -5 + 6x + 8x2 = -1x + x + -2x2 + 2x2 Combine like terms: -1x + x = 0 -5 + 6x + 8x2 = 0 + -2x2 + 2x2 -5 + 6x + 8x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -5 + 6x + 8x2 = 0 Factor a trinomial. (-5 + -4x)(1 + -2x) = 0Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 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 = {-1.25, 0.5}
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