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Simplifying x2 + 27x + 160 = 0 Reorder the terms: 160 + 27x + x2 = 0 Solving 160 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + 27x + -160 + x2 = 0 + -160 Reorder the terms: 160 + -160 + 27x + x2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + 27x + x2 = 0 + -160 27x + x2 = 0 + -160 Combine like terms: 0 + -160 = -160 27x + x2 = -160 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 = -160 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -160 + 182.25 Combine like terms: -160 + 182.25 = 22.25 182.25 + 27x + x2 = 22.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 13.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 13.5 = 4.716990566 Simplifying x + 13.5 = 4.716990566 Reorder the terms: 13.5 + x = 4.716990566 Solving 13.5 + x = 4.716990566 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 = 4.716990566 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 4.716990566 + -13.5 x = 4.716990566 + -13.5 Combine like terms: 4.716990566 + -13.5 = -8.783009434 x = -8.783009434 Simplifying x = -8.783009434Subproblem 2
x + 13.5 = -4.716990566 Simplifying x + 13.5 = -4.716990566 Reorder the terms: 13.5 + x = -4.716990566 Solving 13.5 + x = -4.716990566 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 = -4.716990566 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -4.716990566 + -13.5 x = -4.716990566 + -13.5 Combine like terms: -4.716990566 + -13.5 = -18.216990566 x = -18.216990566 Simplifying x = -18.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.783009434, -18.216990566}
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