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Simplifying 11x2 + 15x + -2684 = 0 Reorder the terms: -2684 + 15x + 11x2 = 0 Solving -2684 + 15x + 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'. -244 + 1.363636364x + x2 = 0 Move the constant term to the right: Add '244' to each side of the equation. -244 + 1.363636364x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + 1.363636364x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + 1.363636364x + x2 = 0 + 244 1.363636364x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 1.363636364x + x2 = 244 The x term is 1.363636364x. Take half its coefficient (0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. 1.363636364x + 0.4648760333 + x2 = 244 + 0.4648760333 Reorder the terms: 0.4648760333 + 1.363636364x + x2 = 244 + 0.4648760333 Combine like terms: 244 + 0.4648760333 = 244.4648760333 0.4648760333 + 1.363636364x + x2 = 244.4648760333 Factor a perfect square on the left side: (x + 0.681818182)(x + 0.681818182) = 244.4648760333 Calculate the square root of the right side: 15.63537259 Break this problem into two subproblems by setting (x + 0.681818182) equal to 15.63537259 and -15.63537259.Subproblem 1
x + 0.681818182 = 15.63537259 Simplifying x + 0.681818182 = 15.63537259 Reorder the terms: 0.681818182 + x = 15.63537259 Solving 0.681818182 + x = 15.63537259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.681818182' to each side of the equation. 0.681818182 + -0.681818182 + x = 15.63537259 + -0.681818182 Combine like terms: 0.681818182 + -0.681818182 = 0.000000000 0.000000000 + x = 15.63537259 + -0.681818182 x = 15.63537259 + -0.681818182 Combine like terms: 15.63537259 + -0.681818182 = 14.953554408 x = 14.953554408 Simplifying x = 14.953554408Subproblem 2
x + 0.681818182 = -15.63537259 Simplifying x + 0.681818182 = -15.63537259 Reorder the terms: 0.681818182 + x = -15.63537259 Solving 0.681818182 + x = -15.63537259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.681818182' to each side of the equation. 0.681818182 + -0.681818182 + x = -15.63537259 + -0.681818182 Combine like terms: 0.681818182 + -0.681818182 = 0.000000000 0.000000000 + x = -15.63537259 + -0.681818182 x = -15.63537259 + -0.681818182 Combine like terms: -15.63537259 + -0.681818182 = -16.317190772 x = -16.317190772 Simplifying x = -16.317190772Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.953554408, -16.317190772}
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