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Simplifying a2 + -2a + -16 = 0 Reorder the terms: -16 + -2a + a2 = 0 Solving -16 + -2a + a2 = 0 Solving for variable 'a'. 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 = 5.123105626 a = 5.123105626 Simplifying a = 5.123105626Subproblem 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 = -3.123105626 a = -3.123105626 Simplifying a = -3.123105626Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.123105626, -3.123105626}
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