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Simplifying a2 + 8a + 11 = 0 Reorder the terms: 11 + 8a + a2 = 0 Solving 11 + 8a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 8a + -11 + a2 = 0 + -11 Reorder the terms: 11 + -11 + 8a + a2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 8a + a2 = 0 + -11 8a + a2 = 0 + -11 Combine like terms: 0 + -11 = -11 8a + a2 = -11 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 = -11 + 16 Reorder the terms: 16 + 8a + a2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + 8a + a2 = 5 Factor a perfect square on the left side: (a + 4)(a + 4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (a + 4) equal to 2.236067978 and -2.236067978.Subproblem 1
a + 4 = 2.236067978 Simplifying a + 4 = 2.236067978 Reorder the terms: 4 + a = 2.236067978 Solving 4 + a = 2.236067978 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 = 2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + a = 2.236067978 + -4 a = 2.236067978 + -4 Combine like terms: 2.236067978 + -4 = -1.763932022 a = -1.763932022 Simplifying a = -1.763932022Subproblem 2
a + 4 = -2.236067978 Simplifying a + 4 = -2.236067978 Reorder the terms: 4 + a = -2.236067978 Solving 4 + a = -2.236067978 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 = -2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + a = -2.236067978 + -4 a = -2.236067978 + -4 Combine like terms: -2.236067978 + -4 = -6.236067978 a = -6.236067978 Simplifying a = -6.236067978Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.763932022, -6.236067978}
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