10n^2-14n-492=0

Solution for 10n^2-14n-492=0 equation:

Simplifying
10n2 + -14n + -492 = 0

Reorder the terms:
-492 + -14n + 10n2 = 0

Solving
-492 + -14n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-246 + -7n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-246 + -7n + 5n2)' equal to zero and attempt to solve:

Simplifying
-246 + -7n + 5n2 = 0

Solving
-246 + -7n + 5n2 = 0

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

Divide each side by '5'.
-49.2 + -1.4n + n2 = 0

Move the constant term to the right:

Add '49.2' to each side of the equation.
-49.2 + -1.4n + 49.2 + n2 = 0 + 49.2

Reorder the terms:
-49.2 + 49.2 + -1.4n + n2 = 0 + 49.2

Combine like terms: -49.2 + 49.2 = 0.0
0.0 + -1.4n + n2 = 0 + 49.2
-1.4n + n2 = 0 + 49.2

Combine like terms: 0 + 49.2 = 49.2
-1.4n + n2 = 49.2

The n term is -1.4n.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4n + 0.49 + n2 = 49.2 + 0.49

Reorder the terms:
0.49 + -1.4n + n2 = 49.2 + 0.49

Combine like terms: 49.2 + 0.49 = 49.69
0.49 + -1.4n + n2 = 49.69

Factor a perfect square on the left side:
(n + -0.7)(n + -0.7) = 49.69

Calculate the square root of the right side: 7.049113419

Break this problem into two subproblems by setting 
(n + -0.7) equal to 7.049113419 and -7.049113419.

Subproblem 1
n + -0.7 = 7.049113419

Simplifying
n + -0.7 = 7.049113419

Reorder the terms:
-0.7 + n = 7.049113419

Solving
-0.7 + n = 7.049113419

Solving for variable 'n'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + n = 7.049113419 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + n = 7.049113419 + 0.7
n = 7.049113419 + 0.7

Combine like terms: 7.049113419 + 0.7 = 7.749113419
n = 7.749113419

Simplifying
n = 7.749113419

Subproblem 2
n + -0.7 = -7.049113419

Simplifying
n + -0.7 = -7.049113419

Reorder the terms:
-0.7 + n = -7.049113419

Solving
-0.7 + n = -7.049113419

Solving for variable 'n'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + n = -7.049113419 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + n = -7.049113419 + 0.7
n = -7.049113419 + 0.7

Combine like terms: -7.049113419 + 0.7 = -6.349113419
n = -6.349113419

Simplifying
n = -6.349113419

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.749113419, -6.349113419}
Solution
n = {7.749113419, -6.349113419}