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Simplifying 84 = x2 + -17x + 66 Reorder the terms: 84 = 66 + -17x + x2 Solving 84 = 66 + -17x + x2 Solving for variable 'x'. Combine like terms: 84 + -66 = 18 18 + 17x + -1x2 = 66 + -17x + x2 + -66 + 17x + -1x2 Reorder the terms: 18 + 17x + -1x2 = 66 + -66 + -17x + 17x + x2 + -1x2 Combine like terms: 66 + -66 = 0 18 + 17x + -1x2 = 0 + -17x + 17x + x2 + -1x2 18 + 17x + -1x2 = -17x + 17x + x2 + -1x2 Combine like terms: -17x + 17x = 0 18 + 17x + -1x2 = 0 + x2 + -1x2 18 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + 17x + -1x2 = 0 Factor a trinomial. (18 + -1x)(1 + x) = 0Subproblem 1
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {18, -1}
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