n^2-3n-35=0

Solution for n^2-3n-35=0 equation:

Simplifying
n2 + -3n + -35 = 0

Reorder the terms:
-35 + -3n + n2 = 0

Solving
-35 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -3n + 35 + n2 = 0 + 35

Reorder the terms:
-35 + 35 + -3n + n2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -3n + n2 = 0 + 35
-3n + n2 = 0 + 35

Combine like terms: 0 + 35 = 35
-3n + n2 = 35

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 = 35 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 35 + 2.25

Combine like terms: 35 + 2.25 = 37.25
2.25 + -3n + n2 = 37.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(n + -1.5) equal to 6.103277808 and -6.103277808.

Subproblem 1
n + -1.5 = 6.103277808

Simplifying
n + -1.5 = 6.103277808

Reorder the terms:
-1.5 + n = 6.103277808

Solving
-1.5 + n = 6.103277808

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 = 6.103277808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 6.103277808 + 1.5
n = 6.103277808 + 1.5

Combine like terms: 6.103277808 + 1.5 = 7.603277808
n = 7.603277808

Simplifying
n = 7.603277808

Subproblem 2
n + -1.5 = -6.103277808

Simplifying
n + -1.5 = -6.103277808

Reorder the terms:
-1.5 + n = -6.103277808

Solving
-1.5 + n = -6.103277808

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 = -6.103277808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -6.103277808 + 1.5
n = -6.103277808 + 1.5

Combine like terms: -6.103277808 + 1.5 = -4.603277808
n = -4.603277808

Simplifying
n = -4.603277808

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.603277808, -4.603277808}