a^2+16a-15=0

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Solution for a^2+16a-15=0 equation: 


Simplifying
a2 + 16a + -15 = 0

Reorder the terms:
-15 + 16a + a2 = 0

Solving
-15 + 16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 16a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + 16a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 16a + a2 = 0 + 15
16a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
16a + a2 = 15

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 = 15 + 64

Reorder the terms:
64 + 16a + a2 = 15 + 64

Combine like terms: 15 + 64 = 79
64 + 16a + a2 = 79

Factor a perfect square on the left side:
(a + 8)(a + 8) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(a + 8) equal to 8.888194417 and -8.888194417.


Subproblem 1
a + 8 = 8.888194417

Simplifying
a + 8 = 8.888194417

Reorder the terms:
8 + a = 8.888194417

Solving
8 + a = 8.888194417

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 = 8.888194417 + -8

Combine like terms: 8 + -8 = 0
0 + a = 8.888194417 + -8
a = 8.888194417 + -8

Combine like terms: 8.888194417 + -8 = 0.888194417
a = 0.888194417

Simplifying
a = 0.888194417


Subproblem 2
a + 8 = -8.888194417

Simplifying
a + 8 = -8.888194417

Reorder the terms:
8 + a = -8.888194417

Solving
8 + a = -8.888194417

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 = -8.888194417 + -8

Combine like terms: 8 + -8 = 0
0 + a = -8.888194417 + -8
a = -8.888194417 + -8

Combine like terms: -8.888194417 + -8 = -16.888194417
a = -16.888194417

Simplifying
a = -16.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.888194417, -16.888194417}

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