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Simplifying x2 + 22x + -121 = 0 Reorder the terms: -121 + 22x + x2 = 0 Solving -121 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 22x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 22x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 22x + x2 = 0 + 121 22x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 22x + x2 = 121 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 = 121 + 121 Reorder the terms: 121 + 22x + x2 = 121 + 121 Combine like terms: 121 + 121 = 242 121 + 22x + x2 = 242 Factor a perfect square on the left side: (x + 11)(x + 11) = 242 Calculate the square root of the right side: 15.556349186 Break this problem into two subproblems by setting (x + 11) equal to 15.556349186 and -15.556349186.Subproblem 1
x + 11 = 15.556349186 Simplifying x + 11 = 15.556349186 Reorder the terms: 11 + x = 15.556349186 Solving 11 + x = 15.556349186 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 = 15.556349186 + -11 Combine like terms: 11 + -11 = 0 0 + x = 15.556349186 + -11 x = 15.556349186 + -11 Combine like terms: 15.556349186 + -11 = 4.556349186 x = 4.556349186 Simplifying x = 4.556349186Subproblem 2
x + 11 = -15.556349186 Simplifying x + 11 = -15.556349186 Reorder the terms: 11 + x = -15.556349186 Solving 11 + x = -15.556349186 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 = -15.556349186 + -11 Combine like terms: 11 + -11 = 0 0 + x = -15.556349186 + -11 x = -15.556349186 + -11 Combine like terms: -15.556349186 + -11 = -26.556349186 x = -26.556349186 Simplifying x = -26.556349186Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.556349186, -26.556349186}
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