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Simplifying 18x2 + -216x + 355 = 0 Reorder the terms: 355 + -216x + 18x2 = 0 Solving 355 + -216x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 19.72222222 + -12x + x2 = 0 Move the constant term to the right: Add '-19.72222222' to each side of the equation. 19.72222222 + -12x + -19.72222222 + x2 = 0 + -19.72222222 Reorder the terms: 19.72222222 + -19.72222222 + -12x + x2 = 0 + -19.72222222 Combine like terms: 19.72222222 + -19.72222222 = 0.00000000 0.00000000 + -12x + x2 = 0 + -19.72222222 -12x + x2 = 0 + -19.72222222 Combine like terms: 0 + -19.72222222 = -19.72222222 -12x + x2 = -19.72222222 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -19.72222222 + 36 Reorder the terms: 36 + -12x + x2 = -19.72222222 + 36 Combine like terms: -19.72222222 + 36 = 16.27777778 36 + -12x + x2 = 16.27777778 Factor a perfect square on the left side: (x + -6)(x + -6) = 16.27777778 Calculate the square root of the right side: 4.034572813 Break this problem into two subproblems by setting (x + -6) equal to 4.034572813 and -4.034572813.Subproblem 1
x + -6 = 4.034572813 Simplifying x + -6 = 4.034572813 Reorder the terms: -6 + x = 4.034572813 Solving -6 + x = 4.034572813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.034572813 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.034572813 + 6 x = 4.034572813 + 6 Combine like terms: 4.034572813 + 6 = 10.034572813 x = 10.034572813 Simplifying x = 10.034572813Subproblem 2
x + -6 = -4.034572813 Simplifying x + -6 = -4.034572813 Reorder the terms: -6 + x = -4.034572813 Solving -6 + x = -4.034572813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.034572813 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.034572813 + 6 x = -4.034572813 + 6 Combine like terms: -4.034572813 + 6 = 1.965427187 x = 1.965427187 Simplifying x = 1.965427187Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.034572813, 1.965427187}
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