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Simplifying 2a + a2 = 16 Solving 2a + a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + 2a + a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 2a + 16 + a2 = 0 + 16 Reorder the terms: -16 + 16 + 2a + a2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2a + a2 = 0 + 16 2a + a2 = 0 + 16 Combine like terms: 0 + 16 = 16 2a + a2 = 16 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 16 + 1 Reorder the terms: 1 + 2a + a2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2a + a2 = 17 Factor a perfect square on the left side: (a + 1)(a + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (a + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
a + 1 = 4.123105626 Simplifying a + 1 = 4.123105626 Reorder the terms: 1 + a = 4.123105626 Solving 1 + a = 4.123105626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + a = 4.123105626 + -1 a = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 a = 3.123105626 Simplifying a = 3.123105626Subproblem 2
a + 1 = -4.123105626 Simplifying a + 1 = -4.123105626 Reorder the terms: 1 + a = -4.123105626 Solving 1 + a = -4.123105626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + a = -4.123105626 + -1 a = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 a = -5.123105626 Simplifying a = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.123105626, -5.123105626}
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