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Simplifying x2 + 22x + -8 = 0 Reorder the terms: -8 + 22x + x2 = 0 Solving -8 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 22x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 22x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 22x + x2 = 0 + 8 22x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 22x + x2 = 8 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 = 8 + 121 Reorder the terms: 121 + 22x + x2 = 8 + 121 Combine like terms: 8 + 121 = 129 121 + 22x + x2 = 129 Factor a perfect square on the left side: (x + 11)(x + 11) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 11) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 11 = 11.357816692 Simplifying x + 11 = 11.357816692 Reorder the terms: 11 + x = 11.357816692 Solving 11 + x = 11.357816692 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 = 11.357816692 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.357816692 + -11 x = 11.357816692 + -11 Combine like terms: 11.357816692 + -11 = 0.357816692 x = 0.357816692 Simplifying x = 0.357816692Subproblem 2
x + 11 = -11.357816692 Simplifying x + 11 = -11.357816692 Reorder the terms: 11 + x = -11.357816692 Solving 11 + x = -11.357816692 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 = -11.357816692 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.357816692 + -11 x = -11.357816692 + -11 Combine like terms: -11.357816692 + -11 = -22.357816692 x = -22.357816692 Simplifying x = -22.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.357816692, -22.357816692}
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