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Simplifying 53.17x2 + -220.68x + 220.68 = 0 Reorder the terms: 220.68 + -220.68x + 53.17x2 = 0 Solving 220.68 + -220.68x + 53.17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 53.17 the coefficient of the squared term: Divide each side by '53.17'. 4.150460786 + -4.150460786x + x2 = 0 Move the constant term to the right: Add '-4.150460786' to each side of the equation. 4.150460786 + -4.150460786x + -4.150460786 + x2 = 0 + -4.150460786 Reorder the terms: 4.150460786 + -4.150460786 + -4.150460786x + x2 = 0 + -4.150460786 Combine like terms: 4.150460786 + -4.150460786 = 0.000000000 0.000000000 + -4.150460786x + x2 = 0 + -4.150460786 -4.150460786x + x2 = 0 + -4.150460786 Combine like terms: 0 + -4.150460786 = -4.150460786 -4.150460786x + x2 = -4.150460786 The x term is -4.150460786x. Take half its coefficient (-2.075230393). Square it (4.306581184) and add it to both sides. Add '4.306581184' to each side of the equation. -4.150460786x + 4.306581184 + x2 = -4.150460786 + 4.306581184 Reorder the terms: 4.306581184 + -4.150460786x + x2 = -4.150460786 + 4.306581184 Combine like terms: -4.150460786 + 4.306581184 = 0.156120398 4.306581184 + -4.150460786x + x2 = 0.156120398 Factor a perfect square on the left side: (x + -2.075230393)(x + -2.075230393) = 0.156120398 Calculate the square root of the right side: 0.395120739 Break this problem into two subproblems by setting (x + -2.075230393) equal to 0.395120739 and -0.395120739.Subproblem 1
x + -2.075230393 = 0.395120739 Simplifying x + -2.075230393 = 0.395120739 Reorder the terms: -2.075230393 + x = 0.395120739 Solving -2.075230393 + x = 0.395120739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.075230393' to each side of the equation. -2.075230393 + 2.075230393 + x = 0.395120739 + 2.075230393 Combine like terms: -2.075230393 + 2.075230393 = 0.000000000 0.000000000 + x = 0.395120739 + 2.075230393 x = 0.395120739 + 2.075230393 Combine like terms: 0.395120739 + 2.075230393 = 2.470351132 x = 2.470351132 Simplifying x = 2.470351132Subproblem 2
x + -2.075230393 = -0.395120739 Simplifying x + -2.075230393 = -0.395120739 Reorder the terms: -2.075230393 + x = -0.395120739 Solving -2.075230393 + x = -0.395120739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.075230393' to each side of the equation. -2.075230393 + 2.075230393 + x = -0.395120739 + 2.075230393 Combine like terms: -2.075230393 + 2.075230393 = 0.000000000 0.000000000 + x = -0.395120739 + 2.075230393 x = -0.395120739 + 2.075230393 Combine like terms: -0.395120739 + 2.075230393 = 1.680109654 x = 1.680109654 Simplifying x = 1.680109654Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.470351132, 1.680109654}
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