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Simplifying 2x2 + 5 + 20x = 20 + 8x2 + x Reorder the terms: 5 + 20x + 2x2 = 20 + 8x2 + x Reorder the terms: 5 + 20x + 2x2 = 20 + x + 8x2 Solving 5 + 20x + 2x2 = 20 + x + 8x2 Solving for variable 'x'. Reorder the terms: 5 + -20 + 20x + -1x + 2x2 + -8x2 = 20 + x + 8x2 + -20 + -1x + -8x2 Combine like terms: 5 + -20 = -15 -15 + 20x + -1x + 2x2 + -8x2 = 20 + x + 8x2 + -20 + -1x + -8x2 Combine like terms: 20x + -1x = 19x -15 + 19x + 2x2 + -8x2 = 20 + x + 8x2 + -20 + -1x + -8x2 Combine like terms: 2x2 + -8x2 = -6x2 -15 + 19x + -6x2 = 20 + x + 8x2 + -20 + -1x + -8x2 Reorder the terms: -15 + 19x + -6x2 = 20 + -20 + x + -1x + 8x2 + -8x2 Combine like terms: 20 + -20 = 0 -15 + 19x + -6x2 = 0 + x + -1x + 8x2 + -8x2 -15 + 19x + -6x2 = x + -1x + 8x2 + -8x2 Combine like terms: x + -1x = 0 -15 + 19x + -6x2 = 0 + 8x2 + -8x2 -15 + 19x + -6x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -15 + 19x + -6x2 = 0 Factor a trinomial. (-5 + 3x)(3 + -2x) = 0Subproblem 1
Set the factor '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 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 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Divide each side by '3'. x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {1.666666667, 1.5}
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