2a^2-66a+252=0

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Solution for 2a^2-66a+252=0 equation: 


Simplifying
2a2 + -66a + 252 = 0

Reorder the terms:
252 + -66a + 2a2 = 0

Solving
252 + -66a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(126 + -33a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(126 + -33a + a2)' equal to zero and attempt to solve:

Simplifying
126 + -33a + a2 = 0

Solving
126 + -33a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-126' to each side of the equation.
126 + -33a + -126 + a2 = 0 + -126

Reorder the terms:
126 + -126 + -33a + a2 = 0 + -126

Combine like terms: 126 + -126 = 0
0 + -33a + a2 = 0 + -126
-33a + a2 = 0 + -126

Combine like terms: 0 + -126 = -126
-33a + a2 = -126

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 = -126 + 272.25

Reorder the terms:
272.25 + -33a + a2 = -126 + 272.25

Combine like terms: -126 + 272.25 = 146.25
272.25 + -33a + a2 = 146.25

Factor a perfect square on the left side:
(a + -16.5)(a + -16.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(a + -16.5) equal to 12.093386622 and -12.093386622.


Subproblem 1
a + -16.5 = 12.093386622

Simplifying
a + -16.5 = 12.093386622

Reorder the terms:
-16.5 + a = 12.093386622

Solving
-16.5 + a = 12.093386622

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 = 12.093386622 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + a = 12.093386622 + 16.5
a = 12.093386622 + 16.5

Combine like terms: 12.093386622 + 16.5 = 28.593386622
a = 28.593386622

Simplifying
a = 28.593386622


Subproblem 2
a + -16.5 = -12.093386622

Simplifying
a + -16.5 = -12.093386622

Reorder the terms:
-16.5 + a = -12.093386622

Solving
-16.5 + a = -12.093386622

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 = -12.093386622 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + a = -12.093386622 + 16.5
a = -12.093386622 + 16.5

Combine like terms: -12.093386622 + 16.5 = 4.406613378
a = 4.406613378

Simplifying
a = 4.406613378


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {28.593386622, 4.406613378}
Solution
a = {28.593386622, 4.406613378}

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