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Simplifying 8x + 4 = 10x2 + 5x Reorder the terms: 4 + 8x = 10x2 + 5x Reorder the terms: 4 + 8x = 5x + 10x2 Solving 4 + 8x = 5x + 10x2 Solving for variable 'x'. Combine like terms: 8x + -5x = 3x 4 + 3x + -10x2 = 5x + 10x2 + -5x + -10x2 Reorder the terms: 4 + 3x + -10x2 = 5x + -5x + 10x2 + -10x2 Combine like terms: 5x + -5x = 0 4 + 3x + -10x2 = 0 + 10x2 + -10x2 4 + 3x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 4 + 3x + -10x2 = 0 Factor a trinomial. (4 + -5x)(1 + 2x) = 0Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8Subproblem 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 = {0.8, -0.5}
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