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Simplifying x2 + -27x + -6 = 0 Reorder the terms: -6 + -27x + x2 = 0 Solving -6 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -27x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -27x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -27x + x2 = 0 + 6 -27x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -27x + x2 = 6 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 = 6 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 6 + 182.25 Combine like terms: 6 + 182.25 = 188.25 182.25 + -27x + x2 = 188.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 188.25 Calculate the square root of the right side: 13.720422734 Break this problem into two subproblems by setting (x + -13.5) equal to 13.720422734 and -13.720422734.Subproblem 1
x + -13.5 = 13.720422734 Simplifying x + -13.5 = 13.720422734 Reorder the terms: -13.5 + x = 13.720422734 Solving -13.5 + x = 13.720422734 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 = 13.720422734 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.720422734 + 13.5 x = 13.720422734 + 13.5 Combine like terms: 13.720422734 + 13.5 = 27.220422734 x = 27.220422734 Simplifying x = 27.220422734Subproblem 2
x + -13.5 = -13.720422734 Simplifying x + -13.5 = -13.720422734 Reorder the terms: -13.5 + x = -13.720422734 Solving -13.5 + x = -13.720422734 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 = -13.720422734 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.720422734 + 13.5 x = -13.720422734 + 13.5 Combine like terms: -13.720422734 + 13.5 = -0.220422734 x = -0.220422734 Simplifying x = -0.220422734Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.220422734, -0.220422734}
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