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Simplifying 0 = x2 + 27x + -81 Reorder the terms: 0 = -81 + 27x + x2 Solving 0 = -81 + 27x + x2 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + -27x + -1x2 = -81 + 27x + x2 + 81 + -27x + -1x2 Reorder the terms: 81 + -27x + -1x2 = -81 + 81 + 27x + -27x + x2 + -1x2 Combine like terms: -81 + 81 = 0 81 + -27x + -1x2 = 0 + 27x + -27x + x2 + -1x2 81 + -27x + -1x2 = 27x + -27x + x2 + -1x2 Combine like terms: 27x + -27x = 0 81 + -27x + -1x2 = 0 + x2 + -1x2 81 + -27x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -27x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 27x + x2 = 0 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 = 2.72498074 x = 2.72498074 Simplifying x = 2.72498074Subproblem 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 = -29.72498074 x = -29.72498074 Simplifying x = -29.72498074Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.72498074, -29.72498074}
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