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Simplifying a2 + 60a + -60 = 0 Reorder the terms: -60 + 60a + a2 = 0 Solving -60 + 60a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 60a + 60 + a2 = 0 + 60 Reorder the terms: -60 + 60 + 60a + a2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 60a + a2 = 0 + 60 60a + a2 = 0 + 60 Combine like terms: 0 + 60 = 60 60a + a2 = 60 The a term is 60a. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60a + 900 + a2 = 60 + 900 Reorder the terms: 900 + 60a + a2 = 60 + 900 Combine like terms: 60 + 900 = 960 900 + 60a + a2 = 960 Factor a perfect square on the left side: (a + 30)(a + 30) = 960 Calculate the square root of the right side: 30.98386677 Break this problem into two subproblems by setting (a + 30) equal to 30.98386677 and -30.98386677.Subproblem 1
a + 30 = 30.98386677 Simplifying a + 30 = 30.98386677 Reorder the terms: 30 + a = 30.98386677 Solving 30 + a = 30.98386677 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + a = 30.98386677 + -30 Combine like terms: 30 + -30 = 0 0 + a = 30.98386677 + -30 a = 30.98386677 + -30 Combine like terms: 30.98386677 + -30 = 0.98386677 a = 0.98386677 Simplifying a = 0.98386677Subproblem 2
a + 30 = -30.98386677 Simplifying a + 30 = -30.98386677 Reorder the terms: 30 + a = -30.98386677 Solving 30 + a = -30.98386677 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + a = -30.98386677 + -30 Combine like terms: 30 + -30 = 0 0 + a = -30.98386677 + -30 a = -30.98386677 + -30 Combine like terms: -30.98386677 + -30 = -60.98386677 a = -60.98386677 Simplifying a = -60.98386677Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.98386677, -60.98386677}
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