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Simplifying 11x2 + x + -54 = 0 Reorder the terms: -54 + x + 11x2 = 0 Solving -54 + x + 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'. -4.909090909 + 0.09090909091x + x2 = 0 Move the constant term to the right: Add '4.909090909' to each side of the equation. -4.909090909 + 0.09090909091x + 4.909090909 + x2 = 0 + 4.909090909 Reorder the terms: -4.909090909 + 4.909090909 + 0.09090909091x + x2 = 0 + 4.909090909 Combine like terms: -4.909090909 + 4.909090909 = 0.000000000 0.000000000 + 0.09090909091x + x2 = 0 + 4.909090909 0.09090909091x + x2 = 0 + 4.909090909 Combine like terms: 0 + 4.909090909 = 4.909090909 0.09090909091x + x2 = 4.909090909 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.09090909091x + 0.25 + x2 = 4.909090909 + 0.25 Reorder the terms: 0.25 + 0.09090909091x + x2 = 4.909090909 + 0.25 Combine like terms: 4.909090909 + 0.25 = 5.159090909 0.25 + 0.09090909091x + x2 = 5.159090909 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.159090909 Calculate the square root of the right side: 2.271363227 Break this problem into two subproblems by setting (x + 0.5) equal to 2.271363227 and -2.271363227.Subproblem 1
x + 0.5 = 2.271363227 Simplifying x + 0.5 = 2.271363227 Reorder the terms: 0.5 + x = 2.271363227 Solving 0.5 + x = 2.271363227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.271363227 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.271363227 + -0.5 x = 2.271363227 + -0.5 Combine like terms: 2.271363227 + -0.5 = 1.771363227 x = 1.771363227 Simplifying x = 1.771363227Subproblem 2
x + 0.5 = -2.271363227 Simplifying x + 0.5 = -2.271363227 Reorder the terms: 0.5 + x = -2.271363227 Solving 0.5 + x = -2.271363227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.271363227 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.271363227 + -0.5 x = -2.271363227 + -0.5 Combine like terms: -2.271363227 + -0.5 = -2.771363227 x = -2.771363227 Simplifying x = -2.771363227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.771363227, -2.771363227}
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