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Simplifying x2 + 22x + 23 = 0 Reorder the terms: 23 + 22x + x2 = 0 Solving 23 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 22x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 22x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 22x + x2 = 0 + -23 22x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 22x + x2 = -23 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 = -23 + 121 Reorder the terms: 121 + 22x + x2 = -23 + 121 Combine like terms: -23 + 121 = 98 121 + 22x + x2 = 98 Factor a perfect square on the left side: (x + 11)(x + 11) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + 11) equal to 9.899494937 and -9.899494937.Subproblem 1
x + 11 = 9.899494937 Simplifying x + 11 = 9.899494937 Reorder the terms: 11 + x = 9.899494937 Solving 11 + x = 9.899494937 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 = 9.899494937 + -11 Combine like terms: 11 + -11 = 0 0 + x = 9.899494937 + -11 x = 9.899494937 + -11 Combine like terms: 9.899494937 + -11 = -1.100505063 x = -1.100505063 Simplifying x = -1.100505063Subproblem 2
x + 11 = -9.899494937 Simplifying x + 11 = -9.899494937 Reorder the terms: 11 + x = -9.899494937 Solving 11 + x = -9.899494937 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 = -9.899494937 + -11 Combine like terms: 11 + -11 = 0 0 + x = -9.899494937 + -11 x = -9.899494937 + -11 Combine like terms: -9.899494937 + -11 = -20.899494937 x = -20.899494937 Simplifying x = -20.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.100505063, -20.899494937}
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