a^2+16a-77=-4

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Solution for a^2+16a-77=-4 equation:


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 = 3.704699911

Subproblem 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 = -19.704699911

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.704699911, -19.704699911}

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