n^2+3n-4=33

Solution for n^2+3n-4=33 equation:

Simplifying
n2 + 3n + -4 = 33

Reorder the terms:
-4 + 3n + n2 = 33

Solving
-4 + 3n + n2 = 33

Solving for variable 'n'.

Reorder the terms:
-4 + -33 + 3n + n2 = 33 + -33

Combine like terms: -4 + -33 = -37
-37 + 3n + n2 = 33 + -33

Combine like terms: 33 + -33 = 0
-37 + 3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 3n + 37 + n2 = 0 + 37

Reorder the terms:
-37 + 37 + 3n + n2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 3n + n2 = 0 + 37
3n + n2 = 0 + 37

Combine like terms: 0 + 37 = 37
3n + n2 = 37

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 37 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 37 + 2.25

Combine like terms: 37 + 2.25 = 39.25
2.25 + 3n + n2 = 39.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(n + 1.5) equal to 6.264982043 and -6.264982043.

Subproblem 1
n + 1.5 = 6.264982043

Simplifying
n + 1.5 = 6.264982043

Reorder the terms:
1.5 + n = 6.264982043

Solving
1.5 + n = 6.264982043

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = 6.264982043 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 6.264982043 + -1.5
n = 6.264982043 + -1.5

Combine like terms: 6.264982043 + -1.5 = 4.764982043
n = 4.764982043

Simplifying
n = 4.764982043

Subproblem 2
n + 1.5 = -6.264982043

Simplifying
n + 1.5 = -6.264982043

Reorder the terms:
1.5 + n = -6.264982043

Solving
1.5 + n = -6.264982043

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = -6.264982043 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -6.264982043 + -1.5
n = -6.264982043 + -1.5

Combine like terms: -6.264982043 + -1.5 = -7.764982043
n = -7.764982043

Simplifying
n = -7.764982043

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.764982043, -7.764982043}