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Simplifying x2 + -27x = 180 Reorder the terms: -27x + x2 = 180 Solving -27x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -27x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -27x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -27x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -27x + x2 = 0 + 180 -27x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -27x + x2 = 180 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 = 180 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 180 + 182.25 Combine like terms: 180 + 182.25 = 362.25 182.25 + -27x + x2 = 362.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 362.25 Calculate the square root of the right side: 19.032866311 Break this problem into two subproblems by setting (x + -13.5) equal to 19.032866311 and -19.032866311.Subproblem 1
x + -13.5 = 19.032866311 Simplifying x + -13.5 = 19.032866311 Reorder the terms: -13.5 + x = 19.032866311 Solving -13.5 + x = 19.032866311 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 = 19.032866311 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 19.032866311 + 13.5 x = 19.032866311 + 13.5 Combine like terms: 19.032866311 + 13.5 = 32.532866311 x = 32.532866311 Simplifying x = 32.532866311Subproblem 2
x + -13.5 = -19.032866311 Simplifying x + -13.5 = -19.032866311 Reorder the terms: -13.5 + x = -19.032866311 Solving -13.5 + x = -19.032866311 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 = -19.032866311 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -19.032866311 + 13.5 x = -19.032866311 + 13.5 Combine like terms: -19.032866311 + 13.5 = -5.532866311 x = -5.532866311 Simplifying x = -5.532866311Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.532866311, -5.532866311}
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