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Simplifying 2x2 + -11x + -570 = 0 Reorder the terms: -570 + -11x + 2x2 = 0 Solving -570 + -11x + 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'. -285 + -5.5x + x2 = 0 Move the constant term to the right: Add '285' to each side of the equation. -285 + -5.5x + 285 + x2 = 0 + 285 Reorder the terms: -285 + 285 + -5.5x + x2 = 0 + 285 Combine like terms: -285 + 285 = 0 0 + -5.5x + x2 = 0 + 285 -5.5x + x2 = 0 + 285 Combine like terms: 0 + 285 = 285 -5.5x + x2 = 285 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 285 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 285 + 7.5625 Combine like terms: 285 + 7.5625 = 292.5625 7.5625 + -5.5x + x2 = 292.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 292.5625 Calculate the square root of the right side: 17.104458483 Break this problem into two subproblems by setting (x + -2.75) equal to 17.104458483 and -17.104458483.Subproblem 1
x + -2.75 = 17.104458483 Simplifying x + -2.75 = 17.104458483 Reorder the terms: -2.75 + x = 17.104458483 Solving -2.75 + x = 17.104458483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 17.104458483 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 17.104458483 + 2.75 x = 17.104458483 + 2.75 Combine like terms: 17.104458483 + 2.75 = 19.854458483 x = 19.854458483 Simplifying x = 19.854458483Subproblem 2
x + -2.75 = -17.104458483 Simplifying x + -2.75 = -17.104458483 Reorder the terms: -2.75 + x = -17.104458483 Solving -2.75 + x = -17.104458483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -17.104458483 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -17.104458483 + 2.75 x = -17.104458483 + 2.75 Combine like terms: -17.104458483 + 2.75 = -14.354458483 x = -14.354458483 Simplifying x = -14.354458483Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.854458483, -14.354458483}
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