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Simplifying x2 + 27x + -16 = 0 Reorder the terms: -16 + 27x + x2 = 0 Solving -16 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 27x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 27x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 27x + x2 = 0 + 16 27x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 27x + x2 = 16 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 = 16 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 16 + 182.25 Combine like terms: 16 + 182.25 = 198.25 182.25 + 27x + x2 = 198.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (x + 13.5) equal to 14.08012784 and -14.08012784.Subproblem 1
x + 13.5 = 14.08012784 Simplifying x + 13.5 = 14.08012784 Reorder the terms: 13.5 + x = 14.08012784 Solving 13.5 + x = 14.08012784 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 = 14.08012784 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 14.08012784 + -13.5 x = 14.08012784 + -13.5 Combine like terms: 14.08012784 + -13.5 = 0.58012784 x = 0.58012784 Simplifying x = 0.58012784Subproblem 2
x + 13.5 = -14.08012784 Simplifying x + 13.5 = -14.08012784 Reorder the terms: 13.5 + x = -14.08012784 Solving 13.5 + x = -14.08012784 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 = -14.08012784 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -14.08012784 + -13.5 x = -14.08012784 + -13.5 Combine like terms: -14.08012784 + -13.5 = -27.58012784 x = -27.58012784 Simplifying x = -27.58012784Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.58012784, -27.58012784}
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