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Simplifying x2 + 27x + 11 = 0 Reorder the terms: 11 + 27x + x2 = 0 Solving 11 + 27x + 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 + 27x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 27x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 27x + x2 = 0 + -11 27x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 27x + x2 = -11 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = -11 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -11 + 182.25 Combine like terms: -11 + 182.25 = 171.25 182.25 + 27x + x2 = 171.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 171.25 Calculate the square root of the right side: 13.086252328 Break this problem into two subproblems by setting (x + 13.5) equal to 13.086252328 and -13.086252328.Subproblem 1
x + 13.5 = 13.086252328 Simplifying x + 13.5 = 13.086252328 Reorder the terms: 13.5 + x = 13.086252328 Solving 13.5 + x = 13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 13.086252328 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.086252328 + -13.5 x = 13.086252328 + -13.5 Combine like terms: 13.086252328 + -13.5 = -0.413747672 x = -0.413747672 Simplifying x = -0.413747672Subproblem 2
x + 13.5 = -13.086252328 Simplifying x + 13.5 = -13.086252328 Reorder the terms: 13.5 + x = -13.086252328 Solving 13.5 + x = -13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -13.086252328 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.086252328 + -13.5 x = -13.086252328 + -13.5 Combine like terms: -13.086252328 + -13.5 = -26.586252328 x = -26.586252328 Simplifying x = -26.586252328Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.413747672, -26.586252328}
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