2n^2+4n-63=0

Solution for 2n^2+4n-63=0 equation:

Simplifying
2n2 + 4n + -63 = 0

Reorder the terms:
-63 + 4n + 2n2 = 0

Solving
-63 + 4n + 2n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-31.5 + 2n + n2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + 2n + 31.5 + n2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + 2n + n2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + 2n + n2 = 0 + 31.5
2n + n2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
2n + n2 = 31.5

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 31.5 + 1

Reorder the terms:
1 + 2n + n2 = 31.5 + 1

Combine like terms: 31.5 + 1 = 32.5
1 + 2n + n2 = 32.5

Factor a perfect square on the left side:
(n + 1)(n + 1) = 32.5

Calculate the square root of the right side: 5.700877125

Break this problem into two subproblems by setting 
(n + 1) equal to 5.700877125 and -5.700877125.

Subproblem 1
n + 1 = 5.700877125

Simplifying
n + 1 = 5.700877125

Reorder the terms:
1 + n = 5.700877125

Solving
1 + n = 5.700877125

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 5.700877125 + -1

Combine like terms: 1 + -1 = 0
0 + n = 5.700877125 + -1
n = 5.700877125 + -1

Combine like terms: 5.700877125 + -1 = 4.700877125
n = 4.700877125

Simplifying
n = 4.700877125

Subproblem 2
n + 1 = -5.700877125

Simplifying
n + 1 = -5.700877125

Reorder the terms:
1 + n = -5.700877125

Solving
1 + n = -5.700877125

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -5.700877125 + -1

Combine like terms: 1 + -1 = 0
0 + n = -5.700877125 + -1
n = -5.700877125 + -1

Combine like terms: -5.700877125 + -1 = -6.700877125
n = -6.700877125

Simplifying
n = -6.700877125

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.700877125, -6.700877125}