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Simplifying 2x2 + 370x + -217 = 0 Reorder the terms: -217 + 370x + 2x2 = 0 Solving -217 + 370x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -108.5 + 185x + x2 = 0 Move the constant term to the right: Add '108.5' to each side of the equation. -108.5 + 185x + 108.5 + x2 = 0 + 108.5 Reorder the terms: -108.5 + 108.5 + 185x + x2 = 0 + 108.5 Combine like terms: -108.5 + 108.5 = 0.0 0.0 + 185x + x2 = 0 + 108.5 185x + x2 = 0 + 108.5 Combine like terms: 0 + 108.5 = 108.5 185x + x2 = 108.5 The x term is 185x. Take half its coefficient (92.5). Square it (8556.25) and add it to both sides. Add '8556.25' to each side of the equation. 185x + 8556.25 + x2 = 108.5 + 8556.25 Reorder the terms: 8556.25 + 185x + x2 = 108.5 + 8556.25 Combine like terms: 108.5 + 8556.25 = 8664.75 8556.25 + 185x + x2 = 8664.75 Factor a perfect square on the left side: (x + 92.5)(x + 92.5) = 8664.75 Calculate the square root of the right side: 93.084638905 Break this problem into two subproblems by setting (x + 92.5) equal to 93.084638905 and -93.084638905.Subproblem 1
x + 92.5 = 93.084638905 Simplifying x + 92.5 = 93.084638905 Reorder the terms: 92.5 + x = 93.084638905 Solving 92.5 + x = 93.084638905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-92.5' to each side of the equation. 92.5 + -92.5 + x = 93.084638905 + -92.5 Combine like terms: 92.5 + -92.5 = 0.0 0.0 + x = 93.084638905 + -92.5 x = 93.084638905 + -92.5 Combine like terms: 93.084638905 + -92.5 = 0.584638905 x = 0.584638905 Simplifying x = 0.584638905Subproblem 2
x + 92.5 = -93.084638905 Simplifying x + 92.5 = -93.084638905 Reorder the terms: 92.5 + x = -93.084638905 Solving 92.5 + x = -93.084638905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-92.5' to each side of the equation. 92.5 + -92.5 + x = -93.084638905 + -92.5 Combine like terms: 92.5 + -92.5 = 0.0 0.0 + x = -93.084638905 + -92.5 x = -93.084638905 + -92.5 Combine like terms: -93.084638905 + -92.5 = -185.584638905 x = -185.584638905 Simplifying x = -185.584638905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.584638905, -185.584638905}
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