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Simplifying x(x + 17) = 2x2 + -4x + 54 Reorder the terms: x(17 + x) = 2x2 + -4x + 54 (17 * x + x * x) = 2x2 + -4x + 54 (17x + x2) = 2x2 + -4x + 54 Reorder the terms: 17x + x2 = 54 + -4x + 2x2 Solving 17x + x2 = 54 + -4x + 2x2 Solving for variable 'x'. Reorder the terms: -54 + 17x + 4x + x2 + -2x2 = 54 + -4x + 2x2 + -54 + 4x + -2x2 Combine like terms: 17x + 4x = 21x -54 + 21x + x2 + -2x2 = 54 + -4x + 2x2 + -54 + 4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -54 + 21x + -1x2 = 54 + -4x + 2x2 + -54 + 4x + -2x2 Reorder the terms: -54 + 21x + -1x2 = 54 + -54 + -4x + 4x + 2x2 + -2x2 Combine like terms: 54 + -54 = 0 -54 + 21x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2 -54 + 21x + -1x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 -54 + 21x + -1x2 = 0 + 2x2 + -2x2 -54 + 21x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -54 + 21x + -1x2 = 0 Factor a trinomial. (-18 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 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 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Simplifying x = 18Subproblem 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 = {18, 3}
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