a^2-33a-30=0

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Solution for a^2-33a-30=0 equation: 


Simplifying
a2 + -33a + -30 = 0

Reorder the terms:
-30 + -33a + a2 = 0

Solving
-30 + -33a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -33a + 30 + a2 = 0 + 30

Reorder the terms:
-30 + 30 + -33a + a2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -33a + a2 = 0 + 30
-33a + a2 = 0 + 30

Combine like terms: 0 + 30 = 30
-33a + a2 = 30

The a term is -33a.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33a + 272.25 + a2 = 30 + 272.25

Reorder the terms:
272.25 + -33a + a2 = 30 + 272.25

Combine like terms: 30 + 272.25 = 302.25
272.25 + -33a + a2 = 302.25

Factor a perfect square on the left side:
(a + -16.5)(a + -16.5) = 302.25

Calculate the square root of the right side: 17.385338651

Break this problem into two subproblems by setting 
(a + -16.5) equal to 17.385338651 and -17.385338651.


Subproblem 1
a + -16.5 = 17.385338651

Simplifying
a + -16.5 = 17.385338651

Reorder the terms:
-16.5 + a = 17.385338651

Solving
-16.5 + a = 17.385338651

Solving for variable 'a'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + a = 17.385338651 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + a = 17.385338651 + 16.5
a = 17.385338651 + 16.5

Combine like terms: 17.385338651 + 16.5 = 33.885338651
a = 33.885338651

Simplifying
a = 33.885338651


Subproblem 2
a + -16.5 = -17.385338651

Simplifying
a + -16.5 = -17.385338651

Reorder the terms:
-16.5 + a = -17.385338651

Solving
-16.5 + a = -17.385338651

Solving for variable 'a'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + a = -17.385338651 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + a = -17.385338651 + 16.5
a = -17.385338651 + 16.5

Combine like terms: -17.385338651 + 16.5 = -0.885338651
a = -0.885338651

Simplifying
a = -0.885338651


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {33.885338651, -0.885338651}

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