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Simplifying x2 + 22x + 115 = 0 Reorder the terms: 115 + 22x + x2 = 0 Solving 115 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-115' to each side of the equation. 115 + 22x + -115 + x2 = 0 + -115 Reorder the terms: 115 + -115 + 22x + x2 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + 22x + x2 = 0 + -115 22x + x2 = 0 + -115 Combine like terms: 0 + -115 = -115 22x + x2 = -115 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -115 + 121 Reorder the terms: 121 + 22x + x2 = -115 + 121 Combine like terms: -115 + 121 = 6 121 + 22x + x2 = 6 Factor a perfect square on the left side: (x + 11)(x + 11) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 11) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 11 = 2.449489743 Simplifying x + 11 = 2.449489743 Reorder the terms: 11 + x = 2.449489743 Solving 11 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 2.449489743 + -11 Combine like terms: 11 + -11 = 0 0 + x = 2.449489743 + -11 x = 2.449489743 + -11 Combine like terms: 2.449489743 + -11 = -8.550510257 x = -8.550510257 Simplifying x = -8.550510257Subproblem 2
x + 11 = -2.449489743 Simplifying x + 11 = -2.449489743 Reorder the terms: 11 + x = -2.449489743 Solving 11 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -2.449489743 + -11 Combine like terms: 11 + -11 = 0 0 + x = -2.449489743 + -11 x = -2.449489743 + -11 Combine like terms: -2.449489743 + -11 = -13.449489743 x = -13.449489743 Simplifying x = -13.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.550510257, -13.449489743}
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