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Simplifying a2 + 8a = -9 Reorder the terms: 8a + a2 = -9 Solving 8a + a2 = -9 Solving for variable 'a'. Reorder the terms: 9 + 8a + a2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8a + -9 + a2 = 0 + -9 Reorder the terms: 9 + -9 + 8a + a2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8a + a2 = 0 + -9 8a + a2 = 0 + -9 Combine like terms: 0 + -9 = -9 8a + a2 = -9 The a term is 8a. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8a + 16 + a2 = -9 + 16 Reorder the terms: 16 + 8a + a2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8a + a2 = 7 Factor a perfect square on the left side: (a + 4)(a + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (a + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
a + 4 = 2.645751311 Simplifying a + 4 = 2.645751311 Reorder the terms: 4 + a = 2.645751311 Solving 4 + a = 2.645751311 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + a = 2.645751311 + -4 a = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 a = -1.354248689 Simplifying a = -1.354248689Subproblem 2
a + 4 = -2.645751311 Simplifying a + 4 = -2.645751311 Reorder the terms: 4 + a = -2.645751311 Solving 4 + a = -2.645751311 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + a = -2.645751311 + -4 a = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 a = -6.645751311 Simplifying a = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.354248689, -6.645751311}
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