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Simplifying 11x2 + -260x + -624 = 0 Reorder the terms: -624 + -260x + 11x2 = 0 Solving -624 + -260x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -56.72727273 + -23.63636364x + x2 = 0 Move the constant term to the right: Add '56.72727273' to each side of the equation. -56.72727273 + -23.63636364x + 56.72727273 + x2 = 0 + 56.72727273 Reorder the terms: -56.72727273 + 56.72727273 + -23.63636364x + x2 = 0 + 56.72727273 Combine like terms: -56.72727273 + 56.72727273 = 0.00000000 0.00000000 + -23.63636364x + x2 = 0 + 56.72727273 -23.63636364x + x2 = 0 + 56.72727273 Combine like terms: 0 + 56.72727273 = 56.72727273 -23.63636364x + x2 = 56.72727273 The x term is -23.63636364x. Take half its coefficient (-11.81818182). Square it (139.6694215) and add it to both sides. Add '139.6694215' to each side of the equation. -23.63636364x + 139.6694215 + x2 = 56.72727273 + 139.6694215 Reorder the terms: 139.6694215 + -23.63636364x + x2 = 56.72727273 + 139.6694215 Combine like terms: 56.72727273 + 139.6694215 = 196.39669423 139.6694215 + -23.63636364x + x2 = 196.39669423 Factor a perfect square on the left side: (x + -11.81818182)(x + -11.81818182) = 196.39669423 Calculate the square root of the right side: 14.01416049 Break this problem into two subproblems by setting (x + -11.81818182) equal to 14.01416049 and -14.01416049.Subproblem 1
x + -11.81818182 = 14.01416049 Simplifying x + -11.81818182 = 14.01416049 Reorder the terms: -11.81818182 + x = 14.01416049 Solving -11.81818182 + x = 14.01416049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.81818182' to each side of the equation. -11.81818182 + 11.81818182 + x = 14.01416049 + 11.81818182 Combine like terms: -11.81818182 + 11.81818182 = 0.00000000 0.00000000 + x = 14.01416049 + 11.81818182 x = 14.01416049 + 11.81818182 Combine like terms: 14.01416049 + 11.81818182 = 25.83234231 x = 25.83234231 Simplifying x = 25.83234231Subproblem 2
x + -11.81818182 = -14.01416049 Simplifying x + -11.81818182 = -14.01416049 Reorder the terms: -11.81818182 + x = -14.01416049 Solving -11.81818182 + x = -14.01416049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.81818182' to each side of the equation. -11.81818182 + 11.81818182 + x = -14.01416049 + 11.81818182 Combine like terms: -11.81818182 + 11.81818182 = 0.00000000 0.00000000 + x = -14.01416049 + 11.81818182 x = -14.01416049 + 11.81818182 Combine like terms: -14.01416049 + 11.81818182 = -2.19597867 x = -2.19597867 Simplifying x = -2.19597867Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.83234231, -2.19597867}
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