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Simplifying (x + -3)(x + -17) = 14x + -238 Reorder the terms: (-3 + x)(x + -17) = 14x + -238 Reorder the terms: (-3 + x)(-17 + x) = 14x + -238 Multiply (-3 + x) * (-17 + x) (-3(-17 + x) + x(-17 + x)) = 14x + -238 ((-17 * -3 + x * -3) + x(-17 + x)) = 14x + -238 ((51 + -3x) + x(-17 + x)) = 14x + -238 (51 + -3x + (-17 * x + x * x)) = 14x + -238 (51 + -3x + (-17x + x2)) = 14x + -238 Combine like terms: -3x + -17x = -20x (51 + -20x + x2) = 14x + -238 Reorder the terms: 51 + -20x + x2 = -238 + 14x Solving 51 + -20x + x2 = -238 + 14x Solving for variable 'x'. Reorder the terms: 51 + 238 + -20x + -14x + x2 = -238 + 14x + 238 + -14x Combine like terms: 51 + 238 = 289 289 + -20x + -14x + x2 = -238 + 14x + 238 + -14x Combine like terms: -20x + -14x = -34x 289 + -34x + x2 = -238 + 14x + 238 + -14x Reorder the terms: 289 + -34x + x2 = -238 + 238 + 14x + -14x Combine like terms: -238 + 238 = 0 289 + -34x + x2 = 0 + 14x + -14x 289 + -34x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 289 + -34x + x2 = 0 Factor a trinomial. (17 + -1x)(17 + -1x) = 0Subproblem 1
Set the factor '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 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 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Divide each side by '-1'. x = 17 Simplifying x = 17Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 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 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Divide each side by '-1'. x = 17 Simplifying x = 17Solution
x = {17, 17}
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