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Simplifying a2 + 16a + -44 = 2 Reorder the terms: -44 + 16a + a2 = 2 Solving -44 + 16a + a2 = 2 Solving for variable 'a'. Reorder the terms: -44 + -2 + 16a + a2 = 2 + -2 Combine like terms: -44 + -2 = -46 -46 + 16a + a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -46 + 16a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 16a + 46 + a2 = 0 + 46 Reorder the terms: -46 + 46 + 16a + a2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 16a + a2 = 0 + 46 16a + a2 = 0 + 46 Combine like terms: 0 + 46 = 46 16a + a2 = 46 The a term is 16a. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16a + 64 + a2 = 46 + 64 Reorder the terms: 64 + 16a + a2 = 46 + 64 Combine like terms: 46 + 64 = 110 64 + 16a + a2 = 110 Factor a perfect square on the left side: (a + 8)(a + 8) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (a + 8) equal to 10.488088482 and -10.488088482.Subproblem 1
a + 8 = 10.488088482 Simplifying a + 8 = 10.488088482 Reorder the terms: 8 + a = 10.488088482 Solving 8 + a = 10.488088482 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 10.488088482 + -8 Combine like terms: 8 + -8 = 0 0 + a = 10.488088482 + -8 a = 10.488088482 + -8 Combine like terms: 10.488088482 + -8 = 2.488088482 a = 2.488088482 Simplifying a = 2.488088482Subproblem 2
a + 8 = -10.488088482 Simplifying a + 8 = -10.488088482 Reorder the terms: 8 + a = -10.488088482 Solving 8 + a = -10.488088482 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -10.488088482 + -8 Combine like terms: 8 + -8 = 0 0 + a = -10.488088482 + -8 a = -10.488088482 + -8 Combine like terms: -10.488088482 + -8 = -18.488088482 a = -18.488088482 Simplifying a = -18.488088482Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.488088482, -18.488088482}
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