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Simplifying x2 + x + -218 = 0 Reorder the terms: -218 + x + x2 = 0 Solving -218 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '218' to each side of the equation. -218 + x + 218 + x2 = 0 + 218 Reorder the terms: -218 + 218 + x + x2 = 0 + 218 Combine like terms: -218 + 218 = 0 0 + x + x2 = 0 + 218 x + x2 = 0 + 218 Combine like terms: 0 + 218 = 218 x + x2 = 218 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 218 + 0.25 Reorder the terms: 0.25 + x + x2 = 218 + 0.25 Combine like terms: 218 + 0.25 = 218.25 0.25 + x + x2 = 218.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 218.25 Calculate the square root of the right side: 14.773286703 Break this problem into two subproblems by setting (x + 0.5) equal to 14.773286703 and -14.773286703.Subproblem 1
x + 0.5 = 14.773286703 Simplifying x + 0.5 = 14.773286703 Reorder the terms: 0.5 + x = 14.773286703 Solving 0.5 + x = 14.773286703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 14.773286703 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.773286703 + -0.5 x = 14.773286703 + -0.5 Combine like terms: 14.773286703 + -0.5 = 14.273286703 x = 14.273286703 Simplifying x = 14.273286703Subproblem 2
x + 0.5 = -14.773286703 Simplifying x + 0.5 = -14.773286703 Reorder the terms: 0.5 + x = -14.773286703 Solving 0.5 + x = -14.773286703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -14.773286703 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.773286703 + -0.5 x = -14.773286703 + -0.5 Combine like terms: -14.773286703 + -0.5 = -15.273286703 x = -15.273286703 Simplifying x = -15.273286703Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.273286703, -15.273286703}
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