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Simplifying 2x2 + 45x + -550 = 0 Reorder the terms: -550 + 45x + 2x2 = 0 Solving -550 + 45x + 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'. -275 + 22.5x + x2 = 0 Move the constant term to the right: Add '275' to each side of the equation. -275 + 22.5x + 275 + x2 = 0 + 275 Reorder the terms: -275 + 275 + 22.5x + x2 = 0 + 275 Combine like terms: -275 + 275 = 0 0 + 22.5x + x2 = 0 + 275 22.5x + x2 = 0 + 275 Combine like terms: 0 + 275 = 275 22.5x + x2 = 275 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 275 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 275 + 126.5625 Combine like terms: 275 + 126.5625 = 401.5625 126.5625 + 22.5x + x2 = 401.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 401.5625 Calculate the square root of the right side: 20.039024427 Break this problem into two subproblems by setting (x + 11.25) equal to 20.039024427 and -20.039024427.Subproblem 1
x + 11.25 = 20.039024427 Simplifying x + 11.25 = 20.039024427 Reorder the terms: 11.25 + x = 20.039024427 Solving 11.25 + x = 20.039024427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 20.039024427 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 20.039024427 + -11.25 x = 20.039024427 + -11.25 Combine like terms: 20.039024427 + -11.25 = 8.789024427 x = 8.789024427 Simplifying x = 8.789024427Subproblem 2
x + 11.25 = -20.039024427 Simplifying x + 11.25 = -20.039024427 Reorder the terms: 11.25 + x = -20.039024427 Solving 11.25 + x = -20.039024427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -20.039024427 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -20.039024427 + -11.25 x = -20.039024427 + -11.25 Combine like terms: -20.039024427 + -11.25 = -31.289024427 x = -31.289024427 Simplifying x = -31.289024427Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.789024427, -31.289024427}
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