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Simplifying x2 + -27x + -360 = 0 Reorder the terms: -360 + -27x + x2 = 0 Solving -360 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + -27x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -27x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -27x + x2 = 0 + 360 -27x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -27x + x2 = 360 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 = 360 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 360 + 182.25 Combine like terms: 360 + 182.25 = 542.25 182.25 + -27x + x2 = 542.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 542.25 Calculate the square root of the right side: 23.286262044 Break this problem into two subproblems by setting (x + -13.5) equal to 23.286262044 and -23.286262044.Subproblem 1
x + -13.5 = 23.286262044 Simplifying x + -13.5 = 23.286262044 Reorder the terms: -13.5 + x = 23.286262044 Solving -13.5 + x = 23.286262044 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 = 23.286262044 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 23.286262044 + 13.5 x = 23.286262044 + 13.5 Combine like terms: 23.286262044 + 13.5 = 36.786262044 x = 36.786262044 Simplifying x = 36.786262044Subproblem 2
x + -13.5 = -23.286262044 Simplifying x + -13.5 = -23.286262044 Reorder the terms: -13.5 + x = -23.286262044 Solving -13.5 + x = -23.286262044 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 = -23.286262044 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -23.286262044 + 13.5 x = -23.286262044 + 13.5 Combine like terms: -23.286262044 + 13.5 = -9.786262044 x = -9.786262044 Simplifying x = -9.786262044Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.786262044, -9.786262044}
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