a^2+2a-36a-9=0

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Solution for a^2+2a-36a-9=0 equation: 


Simplifying
a2 + 2a + -36a + -9 = 0

Reorder the terms:
-9 + 2a + -36a + a2 = 0

Combine like terms: 2a + -36a = -34a
-9 + -34a + a2 = 0

Solving
-9 + -34a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -34a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + -34a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -34a + a2 = 0 + 9
-34a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
-34a + a2 = 9

The a term is -34a.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34a + 289 + a2 = 9 + 289

Reorder the terms:
289 + -34a + a2 = 9 + 289

Combine like terms: 9 + 289 = 298
289 + -34a + a2 = 298

Factor a perfect square on the left side:
(a + -17)(a + -17) = 298

Calculate the square root of the right side: 17.262676502

Break this problem into two subproblems by setting 
(a + -17) equal to 17.262676502 and -17.262676502.


Subproblem 1
a + -17 = 17.262676502

Simplifying
a + -17 = 17.262676502

Reorder the terms:
-17 + a = 17.262676502

Solving
-17 + a = 17.262676502

Solving for variable 'a'.

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

Add '17' to each side of the equation.
-17 + 17 + a = 17.262676502 + 17

Combine like terms: -17 + 17 = 0
0 + a = 17.262676502 + 17
a = 17.262676502 + 17

Combine like terms: 17.262676502 + 17 = 34.262676502
a = 34.262676502

Simplifying
a = 34.262676502


Subproblem 2
a + -17 = -17.262676502

Simplifying
a + -17 = -17.262676502

Reorder the terms:
-17 + a = -17.262676502

Solving
-17 + a = -17.262676502

Solving for variable 'a'.

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

Add '17' to each side of the equation.
-17 + 17 + a = -17.262676502 + 17

Combine like terms: -17 + 17 = 0
0 + a = -17.262676502 + 17
a = -17.262676502 + 17

Combine like terms: -17.262676502 + 17 = -0.262676502
a = -0.262676502

Simplifying
a = -0.262676502


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {34.262676502, -0.262676502}

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