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Simplifying 5x2 + -23x = -3x2 + -2x + -10 Reorder the terms: -23x + 5x2 = -3x2 + -2x + -10 Reorder the terms: -23x + 5x2 = -10 + -2x + -3x2 Solving -23x + 5x2 = -10 + -2x + -3x2 Solving for variable 'x'. Reorder the terms: 10 + -23x + 2x + 5x2 + 3x2 = -10 + -2x + -3x2 + 10 + 2x + 3x2 Combine like terms: -23x + 2x = -21x 10 + -21x + 5x2 + 3x2 = -10 + -2x + -3x2 + 10 + 2x + 3x2 Combine like terms: 5x2 + 3x2 = 8x2 10 + -21x + 8x2 = -10 + -2x + -3x2 + 10 + 2x + 3x2 Reorder the terms: 10 + -21x + 8x2 = -10 + 10 + -2x + 2x + -3x2 + 3x2 Combine like terms: -10 + 10 = 0 10 + -21x + 8x2 = 0 + -2x + 2x + -3x2 + 3x2 10 + -21x + 8x2 = -2x + 2x + -3x2 + 3x2 Combine like terms: -2x + 2x = 0 10 + -21x + 8x2 = 0 + -3x2 + 3x2 10 + -21x + 8x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 10 + -21x + 8x2 = 0 Factor a trinomial. (5 + -8x)(2 + -1x) = 0Subproblem 1
Set the factor '(5 + -8x)' equal to zero and attempt to solve: Simplifying 5 + -8x = 0 Solving 5 + -8x = 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 + -8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x = 0 + -5 -8x = 0 + -5 Combine like terms: 0 + -5 = -5 -8x = -5 Divide each side by '-8'. x = 0.625 Simplifying x = 0.625Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0.625, 2}
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