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Simplifying x2 + 27x + -72 = 0 Reorder the terms: -72 + 27x + x2 = 0 Solving -72 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 27x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 27x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 27x + x2 = 0 + 72 27x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 27x + x2 = 72 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 = 72 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 72 + 182.25 Combine like terms: 72 + 182.25 = 254.25 182.25 + 27x + x2 = 254.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + 13.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + 13.5 = 15.945218719 Simplifying x + 13.5 = 15.945218719 Reorder the terms: 13.5 + x = 15.945218719 Solving 13.5 + x = 15.945218719 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 = 15.945218719 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 15.945218719 + -13.5 x = 15.945218719 + -13.5 Combine like terms: 15.945218719 + -13.5 = 2.445218719 x = 2.445218719 Simplifying x = 2.445218719Subproblem 2
x + 13.5 = -15.945218719 Simplifying x + 13.5 = -15.945218719 Reorder the terms: 13.5 + x = -15.945218719 Solving 13.5 + x = -15.945218719 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 = -15.945218719 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -15.945218719 + -13.5 x = -15.945218719 + -13.5 Combine like terms: -15.945218719 + -13.5 = -29.445218719 x = -29.445218719 Simplifying x = -29.445218719Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.445218719, -29.445218719}
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