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Simplifying a2 + 36a + 8 = 0 Reorder the terms: 8 + 36a + a2 = 0 Solving 8 + 36a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 36a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + 36a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 36a + a2 = 0 + -8 36a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 36a + a2 = -8 The a term is 36a. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36a + 324 + a2 = -8 + 324 Reorder the terms: 324 + 36a + a2 = -8 + 324 Combine like terms: -8 + 324 = 316 324 + 36a + a2 = 316 Factor a perfect square on the left side: (a + 18)(a + 18) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (a + 18) equal to 17.776388835 and -17.776388835.Subproblem 1
a + 18 = 17.776388835 Simplifying a + 18 = 17.776388835 Reorder the terms: 18 + a = 17.776388835 Solving 18 + a = 17.776388835 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + a = 17.776388835 + -18 Combine like terms: 18 + -18 = 0 0 + a = 17.776388835 + -18 a = 17.776388835 + -18 Combine like terms: 17.776388835 + -18 = -0.223611165 a = -0.223611165 Simplifying a = -0.223611165Subproblem 2
a + 18 = -17.776388835 Simplifying a + 18 = -17.776388835 Reorder the terms: 18 + a = -17.776388835 Solving 18 + a = -17.776388835 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + a = -17.776388835 + -18 Combine like terms: 18 + -18 = 0 0 + a = -17.776388835 + -18 a = -17.776388835 + -18 Combine like terms: -17.776388835 + -18 = -35.776388835 a = -35.776388835 Simplifying a = -35.776388835Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.223611165, -35.776388835}
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