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Simplifying 4x2 + -13x + 32 = 8x + 5 Reorder the terms: 32 + -13x + 4x2 = 8x + 5 Reorder the terms: 32 + -13x + 4x2 = 5 + 8x Solving 32 + -13x + 4x2 = 5 + 8x Solving for variable 'x'. Reorder the terms: 32 + -5 + -13x + -8x + 4x2 = 5 + 8x + -5 + -8x Combine like terms: 32 + -5 = 27 27 + -13x + -8x + 4x2 = 5 + 8x + -5 + -8x Combine like terms: -13x + -8x = -21x 27 + -21x + 4x2 = 5 + 8x + -5 + -8x Reorder the terms: 27 + -21x + 4x2 = 5 + -5 + 8x + -8x Combine like terms: 5 + -5 = 0 27 + -21x + 4x2 = 0 + 8x + -8x 27 + -21x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 27 + -21x + 4x2 = 0 Factor a trinomial. (9 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {2.25, 3}
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