a^2-8a-15=0

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Solution for a^2-8a-15=0 equation: 


Simplifying
a2 + -8a + -15 = 0

Reorder the terms:
-15 + -8a + a2 = 0

Solving
-15 + -8a + 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 + -8a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + -8a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8a + a2 = 0 + 15
-8a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8a + a2 = 15

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = 15 + 16

Reorder the terms:
16 + -8a + a2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + -8a + a2 = 31

Factor a perfect square on the left side:
(a + -4)(a + -4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(a + -4) equal to 5.567764363 and -5.567764363.


Subproblem 1
a + -4 = 5.567764363

Simplifying
a + -4 = 5.567764363

Reorder the terms:
-4 + a = 5.567764363

Solving
-4 + a = 5.567764363

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + a = 5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + a = 5.567764363 + 4
a = 5.567764363 + 4

Combine like terms: 5.567764363 + 4 = 9.567764363
a = 9.567764363

Simplifying
a = 9.567764363


Subproblem 2
a + -4 = -5.567764363

Simplifying
a + -4 = -5.567764363

Reorder the terms:
-4 + a = -5.567764363

Solving
-4 + a = -5.567764363

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + a = -5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + a = -5.567764363 + 4
a = -5.567764363 + 4

Combine like terms: -5.567764363 + 4 = -1.567764363
a = -1.567764363

Simplifying
a = -1.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {9.567764363, -1.567764363}

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