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Simplifying x2 + 22x + 119 = 0 Reorder the terms: 119 + 22x + x2 = 0 Solving 119 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-119' to each side of the equation. 119 + 22x + -119 + x2 = 0 + -119 Reorder the terms: 119 + -119 + 22x + x2 = 0 + -119 Combine like terms: 119 + -119 = 0 0 + 22x + x2 = 0 + -119 22x + x2 = 0 + -119 Combine like terms: 0 + -119 = -119 22x + x2 = -119 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 = -119 + 121 Reorder the terms: 121 + 22x + x2 = -119 + 121 Combine like terms: -119 + 121 = 2 121 + 22x + x2 = 2 Factor a perfect square on the left side: (x + 11)(x + 11) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 11) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 11 = 1.414213562 Simplifying x + 11 = 1.414213562 Reorder the terms: 11 + x = 1.414213562 Solving 11 + x = 1.414213562 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 = 1.414213562 + -11 Combine like terms: 11 + -11 = 0 0 + x = 1.414213562 + -11 x = 1.414213562 + -11 Combine like terms: 1.414213562 + -11 = -9.585786438 x = -9.585786438 Simplifying x = -9.585786438Subproblem 2
x + 11 = -1.414213562 Simplifying x + 11 = -1.414213562 Reorder the terms: 11 + x = -1.414213562 Solving 11 + x = -1.414213562 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 = -1.414213562 + -11 Combine like terms: 11 + -11 = 0 0 + x = -1.414213562 + -11 x = -1.414213562 + -11 Combine like terms: -1.414213562 + -11 = -12.414213562 x = -12.414213562 Simplifying x = -12.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.585786438, -12.414213562}
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