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Simplifying 11x2 + -48x + 5 = 0 Reorder the terms: 5 + -48x + 11x2 = 0 Solving 5 + -48x + 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'. 0.4545454545 + -4.363636364x + x2 = 0 Move the constant term to the right: Add '-0.4545454545' to each side of the equation. 0.4545454545 + -4.363636364x + -0.4545454545 + x2 = 0 + -0.4545454545 Reorder the terms: 0.4545454545 + -0.4545454545 + -4.363636364x + x2 = 0 + -0.4545454545 Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000 0.0000000000 + -4.363636364x + x2 = 0 + -0.4545454545 -4.363636364x + x2 = 0 + -0.4545454545 Combine like terms: 0 + -0.4545454545 = -0.4545454545 -4.363636364x + x2 = -0.4545454545 The x term is -4.363636364x. Take half its coefficient (-2.181818182). Square it (4.760330579) and add it to both sides. Add '4.760330579' to each side of the equation. -4.363636364x + 4.760330579 + x2 = -0.4545454545 + 4.760330579 Reorder the terms: 4.760330579 + -4.363636364x + x2 = -0.4545454545 + 4.760330579 Combine like terms: -0.4545454545 + 4.760330579 = 4.3057851245 4.760330579 + -4.363636364x + x2 = 4.3057851245 Factor a perfect square on the left side: (x + -2.181818182)(x + -2.181818182) = 4.3057851245 Calculate the square root of the right side: 2.075038584 Break this problem into two subproblems by setting (x + -2.181818182) equal to 2.075038584 and -2.075038584.Subproblem 1
x + -2.181818182 = 2.075038584 Simplifying x + -2.181818182 = 2.075038584 Reorder the terms: -2.181818182 + x = 2.075038584 Solving -2.181818182 + x = 2.075038584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182 + x = 2.075038584 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + x = 2.075038584 + 2.181818182 x = 2.075038584 + 2.181818182 Combine like terms: 2.075038584 + 2.181818182 = 4.256856766 x = 4.256856766 Simplifying x = 4.256856766Subproblem 2
x + -2.181818182 = -2.075038584 Simplifying x + -2.181818182 = -2.075038584 Reorder the terms: -2.181818182 + x = -2.075038584 Solving -2.181818182 + x = -2.075038584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182 + x = -2.075038584 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + x = -2.075038584 + 2.181818182 x = -2.075038584 + 2.181818182 Combine like terms: -2.075038584 + 2.181818182 = 0.106779598 x = 0.106779598 Simplifying x = 0.106779598Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.256856766, 0.106779598}
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