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Simplifying x2 + -27x + -81 = 0 Reorder the terms: -81 + -27x + x2 = 0 Solving -81 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -27x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -27x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -27x + x2 = 0 + 81 -27x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -27x + x2 = 81 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 = 81 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 81 + 182.25 Combine like terms: 81 + 182.25 = 263.25 182.25 + -27x + x2 = 263.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 263.25 Calculate the square root of the right side: 16.22498074 Break this problem into two subproblems by setting (x + -13.5) equal to 16.22498074 and -16.22498074.Subproblem 1
x + -13.5 = 16.22498074 Simplifying x + -13.5 = 16.22498074 Reorder the terms: -13.5 + x = 16.22498074 Solving -13.5 + x = 16.22498074 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 = 16.22498074 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 16.22498074 + 13.5 x = 16.22498074 + 13.5 Combine like terms: 16.22498074 + 13.5 = 29.72498074 x = 29.72498074 Simplifying x = 29.72498074Subproblem 2
x + -13.5 = -16.22498074 Simplifying x + -13.5 = -16.22498074 Reorder the terms: -13.5 + x = -16.22498074 Solving -13.5 + x = -16.22498074 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 = -16.22498074 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -16.22498074 + 13.5 x = -16.22498074 + 13.5 Combine like terms: -16.22498074 + 13.5 = -2.72498074 x = -2.72498074 Simplifying x = -2.72498074Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.72498074, -2.72498074}
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