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Simplifying -2a2 + 22a + 121 = 0 Reorder the terms: 121 + 22a + -2a2 = 0 Solving 121 + 22a + -2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -60.5 + -11a + a2 = 0 Move the constant term to the right: Add '60.5' to each side of the equation. -60.5 + -11a + 60.5 + a2 = 0 + 60.5 Reorder the terms: -60.5 + 60.5 + -11a + a2 = 0 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + -11a + a2 = 0 + 60.5 -11a + a2 = 0 + 60.5 Combine like terms: 0 + 60.5 = 60.5 -11a + a2 = 60.5 The a term is -11a. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11a + 30.25 + a2 = 60.5 + 30.25 Reorder the terms: 30.25 + -11a + a2 = 60.5 + 30.25 Combine like terms: 60.5 + 30.25 = 90.75 30.25 + -11a + a2 = 90.75 Factor a perfect square on the left side: (a + -5.5)(a + -5.5) = 90.75 Calculate the square root of the right side: 9.526279442 Break this problem into two subproblems by setting (a + -5.5) equal to 9.526279442 and -9.526279442.Subproblem 1
a + -5.5 = 9.526279442 Simplifying a + -5.5 = 9.526279442 Reorder the terms: -5.5 + a = 9.526279442 Solving -5.5 + a = 9.526279442 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 9.526279442 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 9.526279442 + 5.5 a = 9.526279442 + 5.5 Combine like terms: 9.526279442 + 5.5 = 15.026279442 a = 15.026279442 Simplifying a = 15.026279442Subproblem 2
a + -5.5 = -9.526279442 Simplifying a + -5.5 = -9.526279442 Reorder the terms: -5.5 + a = -9.526279442 Solving -5.5 + a = -9.526279442 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -9.526279442 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -9.526279442 + 5.5 a = -9.526279442 + 5.5 Combine like terms: -9.526279442 + 5.5 = -4.026279442 a = -4.026279442 Simplifying a = -4.026279442Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.026279442, -4.026279442}
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