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Simplifying a2 + 16a + -77 = -4 Reorder the terms: -77 + 16a + a2 = -4 Solving -77 + 16a + a2 = -4 Solving for variable 'a'. Reorder the terms: -77 + 4 + 16a + a2 = -4 + 4 Combine like terms: -77 + 4 = -73 -73 + 16a + a2 = -4 + 4 Combine like terms: -4 + 4 = 0 -73 + 16a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 16a + 73 + a2 = 0 + 73 Reorder the terms: -73 + 73 + 16a + a2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 16a + a2 = 0 + 73 16a + a2 = 0 + 73 Combine like terms: 0 + 73 = 73 16a + a2 = 73 The a term is 16a. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16a + 64 + a2 = 73 + 64 Reorder the terms: 64 + 16a + a2 = 73 + 64 Combine like terms: 73 + 64 = 137 64 + 16a + a2 = 137 Factor a perfect square on the left side: (a + 8)(a + 8) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (a + 8) equal to 11.704699911 and -11.704699911.Subproblem 1
a + 8 = 11.704699911 Simplifying a + 8 = 11.704699911 Reorder the terms: 8 + a = 11.704699911 Solving 8 + a = 11.704699911 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 11.704699911 + -8 Combine like terms: 8 + -8 = 0 0 + a = 11.704699911 + -8 a = 11.704699911 + -8 Combine like terms: 11.704699911 + -8 = 3.704699911 a = 3.704699911 Simplifying a = 3.704699911Subproblem 2
a + 8 = -11.704699911 Simplifying a + 8 = -11.704699911 Reorder the terms: 8 + a = -11.704699911 Solving 8 + a = -11.704699911 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -11.704699911 + -8 Combine like terms: 8 + -8 = 0 0 + a = -11.704699911 + -8 a = -11.704699911 + -8 Combine like terms: -11.704699911 + -8 = -19.704699911 a = -19.704699911 Simplifying a = -19.704699911Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.704699911, -19.704699911}
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