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Simplifying a2 + 4a + -2012 = 0 Reorder the terms: -2012 + 4a + a2 = 0 Solving -2012 + 4a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '2012' to each side of the equation. -2012 + 4a + 2012 + a2 = 0 + 2012 Reorder the terms: -2012 + 2012 + 4a + a2 = 0 + 2012 Combine like terms: -2012 + 2012 = 0 0 + 4a + a2 = 0 + 2012 4a + a2 = 0 + 2012 Combine like terms: 0 + 2012 = 2012 4a + a2 = 2012 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 2012 + 4 Reorder the terms: 4 + 4a + a2 = 2012 + 4 Combine like terms: 2012 + 4 = 2016 4 + 4a + a2 = 2016 Factor a perfect square on the left side: (a + 2)(a + 2) = 2016 Calculate the square root of the right side: 44.899888641 Break this problem into two subproblems by setting (a + 2) equal to 44.899888641 and -44.899888641.Subproblem 1
a + 2 = 44.899888641 Simplifying a + 2 = 44.899888641 Reorder the terms: 2 + a = 44.899888641 Solving 2 + a = 44.899888641 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 44.899888641 + -2 Combine like terms: 2 + -2 = 0 0 + a = 44.899888641 + -2 a = 44.899888641 + -2 Combine like terms: 44.899888641 + -2 = 42.899888641 a = 42.899888641 Simplifying a = 42.899888641Subproblem 2
a + 2 = -44.899888641 Simplifying a + 2 = -44.899888641 Reorder the terms: 2 + a = -44.899888641 Solving 2 + a = -44.899888641 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -44.899888641 + -2 Combine like terms: 2 + -2 = 0 0 + a = -44.899888641 + -2 a = -44.899888641 + -2 Combine like terms: -44.899888641 + -2 = -46.899888641 a = -46.899888641 Simplifying a = -46.899888641Solution
The solution to the problem is based on the solutions from the subproblems. a = {42.899888641, -46.899888641}
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