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Simplifying x2 + -11x + -1 = 0 Reorder the terms: -1 + -11x + x2 = 0 Solving -1 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -11x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -11x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -11x + x2 = 0 + 1 -11x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -11x + x2 = 1 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 1 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 1 + 30.25 Combine like terms: 1 + 30.25 = 31.25 30.25 + -11x + x2 = 31.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -5.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -5.5 = 5.590169944 Simplifying x + -5.5 = 5.590169944 Reorder the terms: -5.5 + x = 5.590169944 Solving -5.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.590169944 + 5.5 x = 5.590169944 + 5.5 Combine like terms: 5.590169944 + 5.5 = 11.090169944 x = 11.090169944 Simplifying x = 11.090169944Subproblem 2
x + -5.5 = -5.590169944 Simplifying x + -5.5 = -5.590169944 Reorder the terms: -5.5 + x = -5.590169944 Solving -5.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.590169944 + 5.5 x = -5.590169944 + 5.5 Combine like terms: -5.590169944 + 5.5 = -0.090169944 x = -0.090169944 Simplifying x = -0.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.090169944, -0.090169944}
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