a^2+144a+48=0

Solution for a^2+144a+48=0 equation:

Simplifying
a2 + 144a + 48 = 0

Reorder the terms:
48 + 144a + a2 = 0

Solving
48 + 144a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + 144a + -48 + a2 = 0 + -48

Reorder the terms:
48 + -48 + 144a + a2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + 144a + a2 = 0 + -48
144a + a2 = 0 + -48

Combine like terms: 0 + -48 = -48
144a + a2 = -48

The a term is 144a.  Take half its coefficient (72).
Square it (5184) and add it to both sides.

Add '5184' to each side of the equation.
144a + 5184 + a2 = -48 + 5184

Reorder the terms:
5184 + 144a + a2 = -48 + 5184

Combine like terms: -48 + 5184 = 5136
5184 + 144a + a2 = 5136

Factor a perfect square on the left side:
(a + 72)(a + 72) = 5136

Calculate the square root of the right side: 71.665891469

Break this problem into two subproblems by setting 
(a + 72) equal to 71.665891469 and -71.665891469.

Subproblem 1
a + 72 = 71.665891469

Simplifying
a + 72 = 71.665891469

Reorder the terms:
72 + a = 71.665891469

Solving
72 + a = 71.665891469

Solving for variable 'a'.

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

Add '-72' to each side of the equation.
72 + -72 + a = 71.665891469 + -72

Combine like terms: 72 + -72 = 0
0 + a = 71.665891469 + -72
a = 71.665891469 + -72

Combine like terms: 71.665891469 + -72 = -0.334108531
a = -0.334108531

Simplifying
a = -0.334108531

Subproblem 2
a + 72 = -71.665891469

Simplifying
a + 72 = -71.665891469

Reorder the terms:
72 + a = -71.665891469

Solving
72 + a = -71.665891469

Solving for variable 'a'.

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

Add '-72' to each side of the equation.
72 + -72 + a = -71.665891469 + -72

Combine like terms: 72 + -72 = 0
0 + a = -71.665891469 + -72
a = -71.665891469 + -72

Combine like terms: -71.665891469 + -72 = -143.665891469
a = -143.665891469

Simplifying
a = -143.665891469

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.334108531, -143.665891469}