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Simplifying 11x2 + -5x + -1 = 0 Reorder the terms: -1 + -5x + 11x2 = 0 Solving -1 + -5x + 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'. -0.09090909091 + -0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.4545454545x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.4545454545x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.4545454545x + x2 = 0 + 0.09090909091 -0.4545454545x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.4545454545x + x2 = 0.09090909091 The x term is -0.4545454545x. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545x + 0.05165289257 + x2 = 0.09090909091 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545x + x2 = 0.09090909091 + 0.05165289257 Combine like terms: 0.09090909091 + 0.05165289257 = 0.14256198348 0.05165289257 + -0.4545454545x + x2 = 0.14256198348 Factor a perfect square on the left side: (x + -0.2272727273)(x + -0.2272727273) = 0.14256198348 Calculate the square root of the right side: 0.377573812 Break this problem into two subproblems by setting (x + -0.2272727273) equal to 0.377573812 and -0.377573812.Subproblem 1
x + -0.2272727273 = 0.377573812 Simplifying x + -0.2272727273 = 0.377573812 Reorder the terms: -0.2272727273 + x = 0.377573812 Solving -0.2272727273 + x = 0.377573812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = 0.377573812 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = 0.377573812 + 0.2272727273 x = 0.377573812 + 0.2272727273 Combine like terms: 0.377573812 + 0.2272727273 = 0.6048465393 x = 0.6048465393 Simplifying x = 0.6048465393Subproblem 2
x + -0.2272727273 = -0.377573812 Simplifying x + -0.2272727273 = -0.377573812 Reorder the terms: -0.2272727273 + x = -0.377573812 Solving -0.2272727273 + x = -0.377573812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = -0.377573812 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = -0.377573812 + 0.2272727273 x = -0.377573812 + 0.2272727273 Combine like terms: -0.377573812 + 0.2272727273 = -0.1503010847 x = -0.1503010847 Simplifying x = -0.1503010847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6048465393, -0.1503010847}
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