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Simplifying 8x + 17 = (x + 3)(8x + 17) Reorder the terms: 17 + 8x = (x + 3)(8x + 17) Reorder the terms: 17 + 8x = (3 + x)(8x + 17) Reorder the terms: 17 + 8x = (3 + x)(17 + 8x) Multiply (3 + x) * (17 + 8x) 17 + 8x = (3(17 + 8x) + x(17 + 8x)) 17 + 8x = ((17 * 3 + 8x * 3) + x(17 + 8x)) 17 + 8x = ((51 + 24x) + x(17 + 8x)) 17 + 8x = (51 + 24x + (17 * x + 8x * x)) 17 + 8x = (51 + 24x + (17x + 8x2)) Combine like terms: 24x + 17x = 41x 17 + 8x = (51 + 41x + 8x2) Solving 17 + 8x = 51 + 41x + 8x2 Solving for variable 'x'. Reorder the terms: 17 + -51 + 8x + -41x + -8x2 = 51 + 41x + 8x2 + -51 + -41x + -8x2 Combine like terms: 17 + -51 = -34 -34 + 8x + -41x + -8x2 = 51 + 41x + 8x2 + -51 + -41x + -8x2 Combine like terms: 8x + -41x = -33x -34 + -33x + -8x2 = 51 + 41x + 8x2 + -51 + -41x + -8x2 Reorder the terms: -34 + -33x + -8x2 = 51 + -51 + 41x + -41x + 8x2 + -8x2 Combine like terms: 51 + -51 = 0 -34 + -33x + -8x2 = 0 + 41x + -41x + 8x2 + -8x2 -34 + -33x + -8x2 = 41x + -41x + 8x2 + -8x2 Combine like terms: 41x + -41x = 0 -34 + -33x + -8x2 = 0 + 8x2 + -8x2 -34 + -33x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -34 + -33x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(34 + 33x + 8x2) = 0 Factor a trinomial. -1((17 + 8x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 8x)' equal to zero and attempt to solve: Simplifying 17 + 8x = 0 Solving 17 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 8x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 8x = 0 + -17 8x = 0 + -17 Combine like terms: 0 + -17 = -17 8x = -17 Divide each side by '8'. x = -2.125 Simplifying x = -2.125Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2.125, -2}
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