2a^2-46a-252=0

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Solution for 2a^2-46a-252=0 equation: 


Simplifying
2a2 + -46a + -252 = 0

Reorder the terms:
-252 + -46a + 2a2 = 0

Solving
-252 + -46a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-126 + -23a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-126 + -23a + a2)' equal to zero and attempt to solve:

Simplifying
-126 + -23a + a2 = 0

Solving
-126 + -23a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + -23a + 126 + a2 = 0 + 126

Reorder the terms:
-126 + 126 + -23a + a2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + -23a + a2 = 0 + 126
-23a + a2 = 0 + 126

Combine like terms: 0 + 126 = 126
-23a + a2 = 126

The a term is -23a.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23a + 132.25 + a2 = 126 + 132.25

Reorder the terms:
132.25 + -23a + a2 = 126 + 132.25

Combine like terms: 126 + 132.25 = 258.25
132.25 + -23a + a2 = 258.25

Factor a perfect square on the left side:
(a + -11.5)(a + -11.5) = 258.25

Calculate the square root of the right side: 16.07015868

Break this problem into two subproblems by setting 
(a + -11.5) equal to 16.07015868 and -16.07015868.


Subproblem 1
a + -11.5 = 16.07015868

Simplifying
a + -11.5 = 16.07015868

Reorder the terms:
-11.5 + a = 16.07015868

Solving
-11.5 + a = 16.07015868

Solving for variable 'a'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + a = 16.07015868 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + a = 16.07015868 + 11.5
a = 16.07015868 + 11.5

Combine like terms: 16.07015868 + 11.5 = 27.57015868
a = 27.57015868

Simplifying
a = 27.57015868


Subproblem 2
a + -11.5 = -16.07015868

Simplifying
a + -11.5 = -16.07015868

Reorder the terms:
-11.5 + a = -16.07015868

Solving
-11.5 + a = -16.07015868

Solving for variable 'a'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + a = -16.07015868 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + a = -16.07015868 + 11.5
a = -16.07015868 + 11.5

Combine like terms: -16.07015868 + 11.5 = -4.57015868
a = -4.57015868

Simplifying
a = -4.57015868


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {27.57015868, -4.57015868}
Solution
a = {27.57015868, -4.57015868}

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