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Simplifying 2x2 + -59x + 184 = 0 Reorder the terms: 184 + -59x + 2x2 = 0 Solving 184 + -59x + 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'. 92 + -29.5x + x2 = 0 Move the constant term to the right: Add '-92' to each side of the equation. 92 + -29.5x + -92 + x2 = 0 + -92 Reorder the terms: 92 + -92 + -29.5x + x2 = 0 + -92 Combine like terms: 92 + -92 = 0 0 + -29.5x + x2 = 0 + -92 -29.5x + x2 = 0 + -92 Combine like terms: 0 + -92 = -92 -29.5x + x2 = -92 The x term is -29.5x. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5x + 217.5625 + x2 = -92 + 217.5625 Reorder the terms: 217.5625 + -29.5x + x2 = -92 + 217.5625 Combine like terms: -92 + 217.5625 = 125.5625 217.5625 + -29.5x + x2 = 125.5625 Factor a perfect square on the left side: (x + -14.75)(x + -14.75) = 125.5625 Calculate the square root of the right side: 11.205467416 Break this problem into two subproblems by setting (x + -14.75) equal to 11.205467416 and -11.205467416.Subproblem 1
x + -14.75 = 11.205467416 Simplifying x + -14.75 = 11.205467416 Reorder the terms: -14.75 + x = 11.205467416 Solving -14.75 + x = 11.205467416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = 11.205467416 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = 11.205467416 + 14.75 x = 11.205467416 + 14.75 Combine like terms: 11.205467416 + 14.75 = 25.955467416 x = 25.955467416 Simplifying x = 25.955467416Subproblem 2
x + -14.75 = -11.205467416 Simplifying x + -14.75 = -11.205467416 Reorder the terms: -14.75 + x = -11.205467416 Solving -14.75 + x = -11.205467416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = -11.205467416 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = -11.205467416 + 14.75 x = -11.205467416 + 14.75 Combine like terms: -11.205467416 + 14.75 = 3.544532584 x = 3.544532584 Simplifying x = 3.544532584Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.955467416, 3.544532584}
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