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Simplifying x(x + -17) = 126 Reorder the terms: x(-17 + x) = 126 (-17 * x + x * x) = 126 (-17x + x2) = 126 Solving -17x + x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + -17x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + -17x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + -17x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -17x + x2 = 0 + 126 -17x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 -17x + x2 = 126 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 126 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 126 + 72.25 Combine like terms: 126 + 72.25 = 198.25 72.25 + -17x + x2 = 198.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (x + -8.5) equal to 14.08012784 and -14.08012784.Subproblem 1
x + -8.5 = 14.08012784 Simplifying x + -8.5 = 14.08012784 Reorder the terms: -8.5 + x = 14.08012784 Solving -8.5 + x = 14.08012784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 14.08012784 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 14.08012784 + 8.5 x = 14.08012784 + 8.5 Combine like terms: 14.08012784 + 8.5 = 22.58012784 x = 22.58012784 Simplifying x = 22.58012784Subproblem 2
x + -8.5 = -14.08012784 Simplifying x + -8.5 = -14.08012784 Reorder the terms: -8.5 + x = -14.08012784 Solving -8.5 + x = -14.08012784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -14.08012784 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -14.08012784 + 8.5 x = -14.08012784 + 8.5 Combine like terms: -14.08012784 + 8.5 = -5.58012784 x = -5.58012784 Simplifying x = -5.58012784Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.58012784, -5.58012784}
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