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Simplifying x2 + 22x + -31 = 0 Reorder the terms: -31 + 22x + x2 = 0 Solving -31 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 22x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 22x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 22x + x2 = 0 + 31 22x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 22x + x2 = 31 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 = 31 + 121 Reorder the terms: 121 + 22x + x2 = 31 + 121 Combine like terms: 31 + 121 = 152 121 + 22x + x2 = 152 Factor a perfect square on the left side: (x + 11)(x + 11) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (x + 11) equal to 12.328828006 and -12.328828006.Subproblem 1
x + 11 = 12.328828006 Simplifying x + 11 = 12.328828006 Reorder the terms: 11 + x = 12.328828006 Solving 11 + x = 12.328828006 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 = 12.328828006 + -11 Combine like terms: 11 + -11 = 0 0 + x = 12.328828006 + -11 x = 12.328828006 + -11 Combine like terms: 12.328828006 + -11 = 1.328828006 x = 1.328828006 Simplifying x = 1.328828006Subproblem 2
x + 11 = -12.328828006 Simplifying x + 11 = -12.328828006 Reorder the terms: 11 + x = -12.328828006 Solving 11 + x = -12.328828006 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 = -12.328828006 + -11 Combine like terms: 11 + -11 = 0 0 + x = -12.328828006 + -11 x = -12.328828006 + -11 Combine like terms: -12.328828006 + -11 = -23.328828006 x = -23.328828006 Simplifying x = -23.328828006Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.328828006, -23.328828006}
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