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Simplifying -0.0128x2 + x + 220 = 0 Reorder the terms: 220 + x + -0.0128x2 = 0 Solving 220 + x + -0.0128x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0128 the coefficient of the squared term: Divide each side by '-0.0128'. -17187.5 + -78.125x + x2 = 0 Move the constant term to the right: Add '17187.5' to each side of the equation. -17187.5 + -78.125x + 17187.5 + x2 = 0 + 17187.5 Reorder the terms: -17187.5 + 17187.5 + -78.125x + x2 = 0 + 17187.5 Combine like terms: -17187.5 + 17187.5 = 0.0 0.0 + -78.125x + x2 = 0 + 17187.5 -78.125x + x2 = 0 + 17187.5 Combine like terms: 0 + 17187.5 = 17187.5 -78.125x + x2 = 17187.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -78.125x + 0.25 + x2 = 17187.5 + 0.25 Reorder the terms: 0.25 + -78.125x + x2 = 17187.5 + 0.25 Combine like terms: 17187.5 + 0.25 = 17187.75 0.25 + -78.125x + x2 = 17187.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 17187.75 Calculate the square root of the right side: 131.10205948 Break this problem into two subproblems by setting (x + 0.5) equal to 131.10205948 and -131.10205948.Subproblem 1
x + 0.5 = 131.10205948 Simplifying x + 0.5 = 131.10205948 Reorder the terms: 0.5 + x = 131.10205948 Solving 0.5 + x = 131.10205948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 131.10205948 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 131.10205948 + -0.5 x = 131.10205948 + -0.5 Combine like terms: 131.10205948 + -0.5 = 130.60205948 x = 130.60205948 Simplifying x = 130.60205948Subproblem 2
x + 0.5 = -131.10205948 Simplifying x + 0.5 = -131.10205948 Reorder the terms: 0.5 + x = -131.10205948 Solving 0.5 + x = -131.10205948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -131.10205948 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -131.10205948 + -0.5 x = -131.10205948 + -0.5 Combine like terms: -131.10205948 + -0.5 = -131.60205948 x = -131.60205948 Simplifying x = -131.60205948Solution
The solution to the problem is based on the solutions from the subproblems. x = {130.60205948, -131.60205948}
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