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Simplifying a2 + -22a + 121 = 3 Reorder the terms: 121 + -22a + a2 = 3 Solving 121 + -22a + a2 = 3 Solving for variable 'a'. Reorder the terms: 121 + -3 + -22a + a2 = 3 + -3 Combine like terms: 121 + -3 = 118 118 + -22a + a2 = 3 + -3 Combine like terms: 3 + -3 = 0 118 + -22a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-118' to each side of the equation. 118 + -22a + -118 + a2 = 0 + -118 Reorder the terms: 118 + -118 + -22a + a2 = 0 + -118 Combine like terms: 118 + -118 = 0 0 + -22a + a2 = 0 + -118 -22a + a2 = 0 + -118 Combine like terms: 0 + -118 = -118 -22a + a2 = -118 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 = -118 + 121 Reorder the terms: 121 + -22a + a2 = -118 + 121 Combine like terms: -118 + 121 = 3 121 + -22a + a2 = 3 Factor a perfect square on the left side: (a + -11)(a + -11) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (a + -11) equal to 1.732050808 and -1.732050808.Subproblem 1
a + -11 = 1.732050808 Simplifying a + -11 = 1.732050808 Reorder the terms: -11 + a = 1.732050808 Solving -11 + a = 1.732050808 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 = 1.732050808 + 11 Combine like terms: -11 + 11 = 0 0 + a = 1.732050808 + 11 a = 1.732050808 + 11 Combine like terms: 1.732050808 + 11 = 12.732050808 a = 12.732050808 Simplifying a = 12.732050808Subproblem 2
a + -11 = -1.732050808 Simplifying a + -11 = -1.732050808 Reorder the terms: -11 + a = -1.732050808 Solving -11 + a = -1.732050808 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 = -1.732050808 + 11 Combine like terms: -11 + 11 = 0 0 + a = -1.732050808 + 11 a = -1.732050808 + 11 Combine like terms: -1.732050808 + 11 = 9.267949192 a = 9.267949192 Simplifying a = 9.267949192Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.732050808, 9.267949192}
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