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Simplifying x2 + 41x + 222 = 0 Reorder the terms: 222 + 41x + x2 = 0 Solving 222 + 41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-222' to each side of the equation. 222 + 41x + -222 + x2 = 0 + -222 Reorder the terms: 222 + -222 + 41x + x2 = 0 + -222 Combine like terms: 222 + -222 = 0 0 + 41x + x2 = 0 + -222 41x + x2 = 0 + -222 Combine like terms: 0 + -222 = -222 41x + x2 = -222 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = -222 + 420.25 Reorder the terms: 420.25 + 41x + x2 = -222 + 420.25 Combine like terms: -222 + 420.25 = 198.25 420.25 + 41x + x2 = 198.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (x + 20.5) equal to 14.08012784 and -14.08012784.Subproblem 1
x + 20.5 = 14.08012784 Simplifying x + 20.5 = 14.08012784 Reorder the terms: 20.5 + x = 14.08012784 Solving 20.5 + x = 14.08012784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 14.08012784 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 14.08012784 + -20.5 x = 14.08012784 + -20.5 Combine like terms: 14.08012784 + -20.5 = -6.41987216 x = -6.41987216 Simplifying x = -6.41987216Subproblem 2
x + 20.5 = -14.08012784 Simplifying x + 20.5 = -14.08012784 Reorder the terms: 20.5 + x = -14.08012784 Solving 20.5 + x = -14.08012784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -14.08012784 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -14.08012784 + -20.5 x = -14.08012784 + -20.5 Combine like terms: -14.08012784 + -20.5 = -34.58012784 x = -34.58012784 Simplifying x = -34.58012784Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.41987216, -34.58012784}
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