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Simplifying x2 + 11x + 11 = 0 Reorder the terms: 11 + 11x + x2 = 0 Solving 11 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 11x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 11x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 11x + x2 = 0 + -11 11x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 11x + x2 = -11 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 = -11 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -11 + 30.25 Combine like terms: -11 + 30.25 = 19.25 30.25 + 11x + x2 = 19.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 5.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 5.5 = 4.387482194 Simplifying x + 5.5 = 4.387482194 Reorder the terms: 5.5 + x = 4.387482194 Solving 5.5 + x = 4.387482194 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 = 4.387482194 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.387482194 + -5.5 x = 4.387482194 + -5.5 Combine like terms: 4.387482194 + -5.5 = -1.112517806 x = -1.112517806 Simplifying x = -1.112517806Subproblem 2
x + 5.5 = -4.387482194 Simplifying x + 5.5 = -4.387482194 Reorder the terms: 5.5 + x = -4.387482194 Solving 5.5 + x = -4.387482194 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 = -4.387482194 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.387482194 + -5.5 x = -4.387482194 + -5.5 Combine like terms: -4.387482194 + -5.5 = -9.887482194 x = -9.887482194 Simplifying x = -9.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.112517806, -9.887482194}
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