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Simplifying x2 + 22x + -959 = 0 Reorder the terms: -959 + 22x + x2 = 0 Solving -959 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '959' to each side of the equation. -959 + 22x + 959 + x2 = 0 + 959 Reorder the terms: -959 + 959 + 22x + x2 = 0 + 959 Combine like terms: -959 + 959 = 0 0 + 22x + x2 = 0 + 959 22x + x2 = 0 + 959 Combine like terms: 0 + 959 = 959 22x + x2 = 959 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 = 959 + 121 Reorder the terms: 121 + 22x + x2 = 959 + 121 Combine like terms: 959 + 121 = 1080 121 + 22x + x2 = 1080 Factor a perfect square on the left side: (x + 11)(x + 11) = 1080 Calculate the square root of the right side: 32.86335345 Break this problem into two subproblems by setting (x + 11) equal to 32.86335345 and -32.86335345.Subproblem 1
x + 11 = 32.86335345 Simplifying x + 11 = 32.86335345 Reorder the terms: 11 + x = 32.86335345 Solving 11 + x = 32.86335345 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 = 32.86335345 + -11 Combine like terms: 11 + -11 = 0 0 + x = 32.86335345 + -11 x = 32.86335345 + -11 Combine like terms: 32.86335345 + -11 = 21.86335345 x = 21.86335345 Simplifying x = 21.86335345Subproblem 2
x + 11 = -32.86335345 Simplifying x + 11 = -32.86335345 Reorder the terms: 11 + x = -32.86335345 Solving 11 + x = -32.86335345 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 = -32.86335345 + -11 Combine like terms: 11 + -11 = 0 0 + x = -32.86335345 + -11 x = -32.86335345 + -11 Combine like terms: -32.86335345 + -11 = -43.86335345 x = -43.86335345 Simplifying x = -43.86335345Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.86335345, -43.86335345}
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