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Simplifying x2 + 13x + -27 = 0 Reorder the terms: -27 + 13x + x2 = 0 Solving -27 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 13x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 13x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 13x + x2 = 0 + 27 13x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 13x + x2 = 27 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 27 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 27 + 42.25 Combine like terms: 27 + 42.25 = 69.25 42.25 + 13x + x2 = 69.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + 6.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + 6.5 = 8.321658489 Simplifying x + 6.5 = 8.321658489 Reorder the terms: 6.5 + x = 8.321658489 Solving 6.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 8.321658489 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.321658489 + -6.5 x = 8.321658489 + -6.5 Combine like terms: 8.321658489 + -6.5 = 1.821658489 x = 1.821658489 Simplifying x = 1.821658489Subproblem 2
x + 6.5 = -8.321658489 Simplifying x + 6.5 = -8.321658489 Reorder the terms: 6.5 + x = -8.321658489 Solving 6.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -8.321658489 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.321658489 + -6.5 x = -8.321658489 + -6.5 Combine like terms: -8.321658489 + -6.5 = -14.821658489 x = -14.821658489 Simplifying x = -14.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.821658489, -14.821658489}
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