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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 = 82.94214877 139.6694215 + -23.63636364x + x2 = 82.94214877 Factor a perfect square on the left side: (x + -11.81818182)(x + -11.81818182) = 82.94214877 Calculate the square root of the right side: 9.107258027 Break this problem into two subproblems by setting (x + -11.81818182) equal to 9.107258027 and -9.107258027.Subproblem 1
x + -11.81818182 = 9.107258027 Simplifying x + -11.81818182 = 9.107258027 Reorder the terms: -11.81818182 + x = 9.107258027 Solving -11.81818182 + x = 9.107258027 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 = 9.107258027 + 11.81818182 Combine like terms: -11.81818182 + 11.81818182 = 0.00000000 0.00000000 + x = 9.107258027 + 11.81818182 x = 9.107258027 + 11.81818182 Combine like terms: 9.107258027 + 11.81818182 = 20.925439847 x = 20.925439847 Simplifying x = 20.925439847Subproblem 2
x + -11.81818182 = -9.107258027 Simplifying x + -11.81818182 = -9.107258027 Reorder the terms: -11.81818182 + x = -9.107258027 Solving -11.81818182 + x = -9.107258027 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 = -9.107258027 + 11.81818182 Combine like terms: -11.81818182 + 11.81818182 = 0.00000000 0.00000000 + x = -9.107258027 + 11.81818182 x = -9.107258027 + 11.81818182 Combine like terms: -9.107258027 + 11.81818182 = 2.710923793 x = 2.710923793 Simplifying x = 2.710923793Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.925439847, 2.710923793}
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