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Simplifying x(8x + 1) = 3x2 + -20x + 20 Reorder the terms: x(1 + 8x) = 3x2 + -20x + 20 (1 * x + 8x * x) = 3x2 + -20x + 20 (1x + 8x2) = 3x2 + -20x + 20 Reorder the terms: 1x + 8x2 = 20 + -20x + 3x2 Solving 1x + 8x2 = 20 + -20x + 3x2 Solving for variable 'x'. Reorder the terms: -20 + 1x + 20x + 8x2 + -3x2 = 20 + -20x + 3x2 + -20 + 20x + -3x2 Combine like terms: 1x + 20x = 21x -20 + 21x + 8x2 + -3x2 = 20 + -20x + 3x2 + -20 + 20x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -20 + 21x + 5x2 = 20 + -20x + 3x2 + -20 + 20x + -3x2 Reorder the terms: -20 + 21x + 5x2 = 20 + -20 + -20x + 20x + 3x2 + -3x2 Combine like terms: 20 + -20 = 0 -20 + 21x + 5x2 = 0 + -20x + 20x + 3x2 + -3x2 -20 + 21x + 5x2 = -20x + 20x + 3x2 + -3x2 Combine like terms: -20x + 20x = 0 -20 + 21x + 5x2 = 0 + 3x2 + -3x2 -20 + 21x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -20 + 21x + 5x2 = 0 Factor a trinomial. (-5 + -1x)(4 + -5x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
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 = 0.8Solution
x = {-5, 0.8}
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