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Simplifying x2 + 10x + 11 = 0 Reorder the terms: 11 + 10x + x2 = 0 Solving 11 + 10x + 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 + 10x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 10x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 10x + x2 = 0 + -11 10x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 10x + x2 = -11 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -11 + 25 Reorder the terms: 25 + 10x + x2 = -11 + 25 Combine like terms: -11 + 25 = 14 25 + 10x + x2 = 14 Factor a perfect square on the left side: (x + 5)(x + 5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 5) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 5 = 3.741657387 Simplifying x + 5 = 3.741657387 Reorder the terms: 5 + x = 3.741657387 Solving 5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.741657387 + -5 x = 3.741657387 + -5 Combine like terms: 3.741657387 + -5 = -1.258342613 x = -1.258342613 Simplifying x = -1.258342613Subproblem 2
x + 5 = -3.741657387 Simplifying x + 5 = -3.741657387 Reorder the terms: 5 + x = -3.741657387 Solving 5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.741657387 + -5 x = -3.741657387 + -5 Combine like terms: -3.741657387 + -5 = -8.741657387 x = -8.741657387 Simplifying x = -8.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.258342613, -8.741657387}
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