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Simplifying x2 + 11x + 13 = 0 Reorder the terms: 13 + 11x + x2 = 0 Solving 13 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 11x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 11x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 11x + x2 = 0 + -13 11x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 11x + x2 = -13 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 = -13 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -13 + 30.25 Combine like terms: -13 + 30.25 = 17.25 30.25 + 11x + x2 = 17.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 5.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 5.5 = 4.153311931 Simplifying x + 5.5 = 4.153311931 Reorder the terms: 5.5 + x = 4.153311931 Solving 5.5 + x = 4.153311931 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 = 4.153311931 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.153311931 + -5.5 x = 4.153311931 + -5.5 Combine like terms: 4.153311931 + -5.5 = -1.346688069 x = -1.346688069 Simplifying x = -1.346688069Subproblem 2
x + 5.5 = -4.153311931 Simplifying x + 5.5 = -4.153311931 Reorder the terms: 5.5 + x = -4.153311931 Solving 5.5 + x = -4.153311931 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 = -4.153311931 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.153311931 + -5.5 x = -4.153311931 + -5.5 Combine like terms: -4.153311931 + -5.5 = -9.653311931 x = -9.653311931 Simplifying x = -9.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.346688069, -9.653311931}
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