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Simplifying x2 + -116x + 58 = 0 Reorder the terms: 58 + -116x + x2 = 0 Solving 58 + -116x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -116x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -116x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -116x + x2 = 0 + -58 -116x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -116x + x2 = -58 The x term is -116x. Take half its coefficient (-58). Square it (3364) and add it to both sides. Add '3364' to each side of the equation. -116x + 3364 + x2 = -58 + 3364 Reorder the terms: 3364 + -116x + x2 = -58 + 3364 Combine like terms: -58 + 3364 = 3306 3364 + -116x + x2 = 3306 Factor a perfect square on the left side: (x + -58)(x + -58) = 3306 Calculate the square root of the right side: 57.497826046 Break this problem into two subproblems by setting (x + -58) equal to 57.497826046 and -57.497826046.Subproblem 1
x + -58 = 57.497826046 Simplifying x + -58 = 57.497826046 Reorder the terms: -58 + x = 57.497826046 Solving -58 + x = 57.497826046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = 57.497826046 + 58 Combine like terms: -58 + 58 = 0 0 + x = 57.497826046 + 58 x = 57.497826046 + 58 Combine like terms: 57.497826046 + 58 = 115.497826046 x = 115.497826046 Simplifying x = 115.497826046Subproblem 2
x + -58 = -57.497826046 Simplifying x + -58 = -57.497826046 Reorder the terms: -58 + x = -57.497826046 Solving -58 + x = -57.497826046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = -57.497826046 + 58 Combine like terms: -58 + 58 = 0 0 + x = -57.497826046 + 58 x = -57.497826046 + 58 Combine like terms: -57.497826046 + 58 = 0.502173954 x = 0.502173954 Simplifying x = 0.502173954Solution
The solution to the problem is based on the solutions from the subproblems. x = {115.497826046, 0.502173954}
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