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Simplifying 11x2 = 15x + 5 Reorder the terms: 11x2 = 5 + 15x Solving 11x2 = 5 + 15x Solving for variable 'x'. Reorder the terms: -5 + -15x + 11x2 = 5 + 15x + -5 + -15x Reorder the terms: -5 + -15x + 11x2 = 5 + -5 + 15x + -15x Combine like terms: 5 + -5 = 0 -5 + -15x + 11x2 = 0 + 15x + -15x -5 + -15x + 11x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -5 + -15x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + -1.363636364x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -1.363636364x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -1.363636364x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -1.363636364x + x2 = 0 + 0.4545454545 -1.363636364x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -1.363636364x + x2 = 0.4545454545 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 = 0.4545454545 + 0.4648760333 Reorder the terms: 0.4648760333 + -1.363636364x + x2 = 0.4545454545 + 0.4648760333 Combine like terms: 0.4545454545 + 0.4648760333 = 0.9194214878 0.4648760333 + -1.363636364x + x2 = 0.9194214878 Factor a perfect square on the left side: (x + -0.681818182)(x + -0.681818182) = 0.9194214878 Calculate the square root of the right side: 0.958864687 Break this problem into two subproblems by setting (x + -0.681818182) equal to 0.958864687 and -0.958864687.Subproblem 1
x + -0.681818182 = 0.958864687 Simplifying x + -0.681818182 = 0.958864687 Reorder the terms: -0.681818182 + x = 0.958864687 Solving -0.681818182 + x = 0.958864687 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 = 0.958864687 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = 0.958864687 + 0.681818182 x = 0.958864687 + 0.681818182 Combine like terms: 0.958864687 + 0.681818182 = 1.640682869 x = 1.640682869 Simplifying x = 1.640682869Subproblem 2
x + -0.681818182 = -0.958864687 Simplifying x + -0.681818182 = -0.958864687 Reorder the terms: -0.681818182 + x = -0.958864687 Solving -0.681818182 + x = -0.958864687 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 = -0.958864687 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = -0.958864687 + 0.681818182 x = -0.958864687 + 0.681818182 Combine like terms: -0.958864687 + 0.681818182 = -0.277046505 x = -0.277046505 Simplifying x = -0.277046505Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.640682869, -0.277046505}
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