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Simplifying 11x2 + 112x + 256 = 0 Reorder the terms: 256 + 112x + 11x2 = 0 Solving 256 + 112x + 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'. 23.27272727 + 10.18181818x + x2 = 0 Move the constant term to the right: Add '-23.27272727' to each side of the equation. 23.27272727 + 10.18181818x + -23.27272727 + x2 = 0 + -23.27272727 Reorder the terms: 23.27272727 + -23.27272727 + 10.18181818x + x2 = 0 + -23.27272727 Combine like terms: 23.27272727 + -23.27272727 = 0.00000000 0.00000000 + 10.18181818x + x2 = 0 + -23.27272727 10.18181818x + x2 = 0 + -23.27272727 Combine like terms: 0 + -23.27272727 = -23.27272727 10.18181818x + x2 = -23.27272727 The x term is 10.18181818x. Take half its coefficient (5.09090909). Square it (25.91735536) and add it to both sides. Add '25.91735536' to each side of the equation. 10.18181818x + 25.91735536 + x2 = -23.27272727 + 25.91735536 Reorder the terms: 25.91735536 + 10.18181818x + x2 = -23.27272727 + 25.91735536 Combine like terms: -23.27272727 + 25.91735536 = 2.64462809 25.91735536 + 10.18181818x + x2 = 2.64462809 Factor a perfect square on the left side: (x + 5.09090909)(x + 5.09090909) = 2.64462809 Calculate the square root of the right side: 1.626231254 Break this problem into two subproblems by setting (x + 5.09090909) equal to 1.626231254 and -1.626231254.Subproblem 1
x + 5.09090909 = 1.626231254 Simplifying x + 5.09090909 = 1.626231254 Reorder the terms: 5.09090909 + x = 1.626231254 Solving 5.09090909 + x = 1.626231254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.09090909' to each side of the equation. 5.09090909 + -5.09090909 + x = 1.626231254 + -5.09090909 Combine like terms: 5.09090909 + -5.09090909 = 0.00000000 0.00000000 + x = 1.626231254 + -5.09090909 x = 1.626231254 + -5.09090909 Combine like terms: 1.626231254 + -5.09090909 = -3.464677836 x = -3.464677836 Simplifying x = -3.464677836Subproblem 2
x + 5.09090909 = -1.626231254 Simplifying x + 5.09090909 = -1.626231254 Reorder the terms: 5.09090909 + x = -1.626231254 Solving 5.09090909 + x = -1.626231254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.09090909' to each side of the equation. 5.09090909 + -5.09090909 + x = -1.626231254 + -5.09090909 Combine like terms: 5.09090909 + -5.09090909 = 0.00000000 0.00000000 + x = -1.626231254 + -5.09090909 x = -1.626231254 + -5.09090909 Combine like terms: -1.626231254 + -5.09090909 = -6.717140344 x = -6.717140344 Simplifying x = -6.717140344Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.464677836, -6.717140344}
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