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Simplifying -1a2 + -22a + 121 = 0 Reorder the terms: 121 + -22a + -1a2 = 0 Solving 121 + -22a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -121 + 22a + a2 = 0 Move the constant term to the right: Add '121' to each side of the equation. -121 + 22a + 121 + a2 = 0 + 121 Reorder the terms: -121 + 121 + 22a + a2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 22a + a2 = 0 + 121 22a + a2 = 0 + 121 Combine like terms: 0 + 121 = 121 22a + a2 = 121 The a term is 22a. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22a + 121 + a2 = 121 + 121 Reorder the terms: 121 + 22a + a2 = 121 + 121 Combine like terms: 121 + 121 = 242 121 + 22a + a2 = 242 Factor a perfect square on the left side: (a + 11)(a + 11) = 242 Calculate the square root of the right side: 15.556349186 Break this problem into two subproblems by setting (a + 11) equal to 15.556349186 and -15.556349186.Subproblem 1
a + 11 = 15.556349186 Simplifying a + 11 = 15.556349186 Reorder the terms: 11 + a = 15.556349186 Solving 11 + a = 15.556349186 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + a = 15.556349186 + -11 Combine like terms: 11 + -11 = 0 0 + a = 15.556349186 + -11 a = 15.556349186 + -11 Combine like terms: 15.556349186 + -11 = 4.556349186 a = 4.556349186 Simplifying a = 4.556349186Subproblem 2
a + 11 = -15.556349186 Simplifying a + 11 = -15.556349186 Reorder the terms: 11 + a = -15.556349186 Solving 11 + a = -15.556349186 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + a = -15.556349186 + -11 Combine like terms: 11 + -11 = 0 0 + a = -15.556349186 + -11 a = -15.556349186 + -11 Combine like terms: -15.556349186 + -11 = -26.556349186 a = -26.556349186 Simplifying a = -26.556349186Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.556349186, -26.556349186}
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