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Simplifying x2 + 27x + -576 = 0 Reorder the terms: -576 + 27x + x2 = 0 Solving -576 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 27x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + 27x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 27x + x2 = 0 + 576 27x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 27x + x2 = 576 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 = 576 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 576 + 182.25 Combine like terms: 576 + 182.25 = 758.25 182.25 + 27x + x2 = 758.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 758.25 Calculate the square root of the right side: 27.536339626 Break this problem into two subproblems by setting (x + 13.5) equal to 27.536339626 and -27.536339626.Subproblem 1
x + 13.5 = 27.536339626 Simplifying x + 13.5 = 27.536339626 Reorder the terms: 13.5 + x = 27.536339626 Solving 13.5 + x = 27.536339626 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 = 27.536339626 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 27.536339626 + -13.5 x = 27.536339626 + -13.5 Combine like terms: 27.536339626 + -13.5 = 14.036339626 x = 14.036339626 Simplifying x = 14.036339626Subproblem 2
x + 13.5 = -27.536339626 Simplifying x + 13.5 = -27.536339626 Reorder the terms: 13.5 + x = -27.536339626 Solving 13.5 + x = -27.536339626 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 = -27.536339626 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -27.536339626 + -13.5 x = -27.536339626 + -13.5 Combine like terms: -27.536339626 + -13.5 = -41.036339626 x = -41.036339626 Simplifying x = -41.036339626Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.036339626, -41.036339626}
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