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Simplifying a2 + 11a + -72 = 0 Reorder the terms: -72 + 11a + a2 = 0 Solving -72 + 11a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 11a + 72 + a2 = 0 + 72 Reorder the terms: -72 + 72 + 11a + a2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 11a + a2 = 0 + 72 11a + a2 = 0 + 72 Combine like terms: 0 + 72 = 72 11a + a2 = 72 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 = 72 + 30.25 Reorder the terms: 30.25 + 11a + a2 = 72 + 30.25 Combine like terms: 72 + 30.25 = 102.25 30.25 + 11a + a2 = 102.25 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (a + 5.5) equal to 10.111874208 and -10.111874208.Subproblem 1
a + 5.5 = 10.111874208 Simplifying a + 5.5 = 10.111874208 Reorder the terms: 5.5 + a = 10.111874208 Solving 5.5 + a = 10.111874208 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 = 10.111874208 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 10.111874208 + -5.5 a = 10.111874208 + -5.5 Combine like terms: 10.111874208 + -5.5 = 4.611874208 a = 4.611874208 Simplifying a = 4.611874208Subproblem 2
a + 5.5 = -10.111874208 Simplifying a + 5.5 = -10.111874208 Reorder the terms: 5.5 + a = -10.111874208 Solving 5.5 + a = -10.111874208 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 = -10.111874208 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -10.111874208 + -5.5 a = -10.111874208 + -5.5 Combine like terms: -10.111874208 + -5.5 = -15.611874208 a = -15.611874208 Simplifying a = -15.611874208Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.611874208, -15.611874208}
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