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Simplifying 2x2 + 17x + -185 = 0 Reorder the terms: -185 + 17x + 2x2 = 0 Solving -185 + 17x + 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'. -92.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '92.5' to each side of the equation. -92.5 + 8.5x + 92.5 + x2 = 0 + 92.5 Reorder the terms: -92.5 + 92.5 + 8.5x + x2 = 0 + 92.5 Combine like terms: -92.5 + 92.5 = 0.0 0.0 + 8.5x + x2 = 0 + 92.5 8.5x + x2 = 0 + 92.5 Combine like terms: 0 + 92.5 = 92.5 8.5x + x2 = 92.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 92.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 92.5 + 18.0625 Combine like terms: 92.5 + 18.0625 = 110.5625 18.0625 + 8.5x + x2 = 110.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 110.5625 Calculate the square root of the right side: 10.514870422 Break this problem into two subproblems by setting (x + 4.25) equal to 10.514870422 and -10.514870422.Subproblem 1
x + 4.25 = 10.514870422 Simplifying x + 4.25 = 10.514870422 Reorder the terms: 4.25 + x = 10.514870422 Solving 4.25 + x = 10.514870422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 10.514870422 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 10.514870422 + -4.25 x = 10.514870422 + -4.25 Combine like terms: 10.514870422 + -4.25 = 6.264870422 x = 6.264870422 Simplifying x = 6.264870422Subproblem 2
x + 4.25 = -10.514870422 Simplifying x + 4.25 = -10.514870422 Reorder the terms: 4.25 + x = -10.514870422 Solving 4.25 + x = -10.514870422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -10.514870422 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -10.514870422 + -4.25 x = -10.514870422 + -4.25 Combine like terms: -10.514870422 + -4.25 = -14.764870422 x = -14.764870422 Simplifying x = -14.764870422Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.264870422, -14.764870422}
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