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Simplifying 165 = (8 + 2x)(10 + x + (3x + -1)) Reorder the terms: 165 = (8 + 2x)(10 + x + (-1 + 3x)) Remove parenthesis around (-1 + 3x) 165 = (8 + 2x)(10 + x + -1 + 3x) Reorder the terms: 165 = (8 + 2x)(10 + -1 + x + 3x) Combine like terms: 10 + -1 = 9 165 = (8 + 2x)(9 + x + 3x) Combine like terms: x + 3x = 4x 165 = (8 + 2x)(9 + 4x) Multiply (8 + 2x) * (9 + 4x) 165 = (8(9 + 4x) + 2x * (9 + 4x)) 165 = ((9 * 8 + 4x * 8) + 2x * (9 + 4x)) 165 = ((72 + 32x) + 2x * (9 + 4x)) 165 = (72 + 32x + (9 * 2x + 4x * 2x)) 165 = (72 + 32x + (18x + 8x2)) Combine like terms: 32x + 18x = 50x 165 = (72 + 50x + 8x2) Solving 165 = 72 + 50x + 8x2 Solving for variable 'x'. Combine like terms: 165 + -72 = 93 93 + -50x + -8x2 = 72 + 50x + 8x2 + -72 + -50x + -8x2 Reorder the terms: 93 + -50x + -8x2 = 72 + -72 + 50x + -50x + 8x2 + -8x2 Combine like terms: 72 + -72 = 0 93 + -50x + -8x2 = 0 + 50x + -50x + 8x2 + -8x2 93 + -50x + -8x2 = 50x + -50x + 8x2 + -8x2 Combine like terms: 50x + -50x = 0 93 + -50x + -8x2 = 0 + 8x2 + -8x2 93 + -50x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 93 + -50x + -8x2 = 0 Factor a trinomial. (3 + -2x)(31 + 4x) = 0Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(31 + 4x)' equal to zero and attempt to solve: Simplifying 31 + 4x = 0 Solving 31 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 4x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 4x = 0 + -31 4x = 0 + -31 Combine like terms: 0 + -31 = -31 4x = -31 Divide each side by '4'. x = -7.75 Simplifying x = -7.75Solution
x = {1.5, -7.75}
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