a^2-48a+336=0

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Solution for a^2-48a+336=0 equation: 


Simplifying
a2 + -48a + 336 = 0

Reorder the terms:
336 + -48a + a2 = 0

Solving
336 + -48a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-336' to each side of the equation.
336 + -48a + -336 + a2 = 0 + -336

Reorder the terms:
336 + -336 + -48a + a2 = 0 + -336

Combine like terms: 336 + -336 = 0
0 + -48a + a2 = 0 + -336
-48a + a2 = 0 + -336

Combine like terms: 0 + -336 = -336
-48a + a2 = -336

The a term is -48a.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48a + 576 + a2 = -336 + 576

Reorder the terms:
576 + -48a + a2 = -336 + 576

Combine like terms: -336 + 576 = 240
576 + -48a + a2 = 240

Factor a perfect square on the left side:
(a + -24)(a + -24) = 240

Calculate the square root of the right side: 15.491933385

Break this problem into two subproblems by setting 
(a + -24) equal to 15.491933385 and -15.491933385.


Subproblem 1
a + -24 = 15.491933385

Simplifying
a + -24 = 15.491933385

Reorder the terms:
-24 + a = 15.491933385

Solving
-24 + a = 15.491933385

Solving for variable 'a'.

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

Add '24' to each side of the equation.
-24 + 24 + a = 15.491933385 + 24

Combine like terms: -24 + 24 = 0
0 + a = 15.491933385 + 24
a = 15.491933385 + 24

Combine like terms: 15.491933385 + 24 = 39.491933385
a = 39.491933385

Simplifying
a = 39.491933385


Subproblem 2
a + -24 = -15.491933385

Simplifying
a + -24 = -15.491933385

Reorder the terms:
-24 + a = -15.491933385

Solving
-24 + a = -15.491933385

Solving for variable 'a'.

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

Add '24' to each side of the equation.
-24 + 24 + a = -15.491933385 + 24

Combine like terms: -24 + 24 = 0
0 + a = -15.491933385 + 24
a = -15.491933385 + 24

Combine like terms: -15.491933385 + 24 = 8.508066615
a = 8.508066615

Simplifying
a = 8.508066615


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {39.491933385, 8.508066615}

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