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Simplifying x2 + 27x + 59 = 0 Reorder the terms: 59 + 27x + x2 = 0 Solving 59 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 27x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 27x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 27x + x2 = 0 + -59 27x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 27x + x2 = -59 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 = -59 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -59 + 182.25 Combine like terms: -59 + 182.25 = 123.25 182.25 + 27x + x2 = 123.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 123.25 Calculate the square root of the right side: 11.101801656 Break this problem into two subproblems by setting (x + 13.5) equal to 11.101801656 and -11.101801656.Subproblem 1
x + 13.5 = 11.101801656 Simplifying x + 13.5 = 11.101801656 Reorder the terms: 13.5 + x = 11.101801656 Solving 13.5 + x = 11.101801656 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 = 11.101801656 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 11.101801656 + -13.5 x = 11.101801656 + -13.5 Combine like terms: 11.101801656 + -13.5 = -2.398198344 x = -2.398198344 Simplifying x = -2.398198344Subproblem 2
x + 13.5 = -11.101801656 Simplifying x + 13.5 = -11.101801656 Reorder the terms: 13.5 + x = -11.101801656 Solving 13.5 + x = -11.101801656 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 = -11.101801656 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -11.101801656 + -13.5 x = -11.101801656 + -13.5 Combine like terms: -11.101801656 + -13.5 = -24.601801656 x = -24.601801656 Simplifying x = -24.601801656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.398198344, -24.601801656}
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