8n^2-4n+2=5n-11

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Solution for 8n^2-4n+2=5n-11 equation:


Simplifying
8n2 + -4n + 2 = 5n + -11

Reorder the terms:
2 + -4n + 8n2 = 5n + -11

Reorder the terms:
2 + -4n + 8n2 = -11 + 5n

Solving
2 + -4n + 8n2 = -11 + 5n

Solving for variable 'n'.

Reorder the terms:
2 + 11 + -4n + -5n + 8n2 = -11 + 5n + 11 + -5n

Combine like terms: 2 + 11 = 13
13 + -4n + -5n + 8n2 = -11 + 5n + 11 + -5n

Combine like terms: -4n + -5n = -9n
13 + -9n + 8n2 = -11 + 5n + 11 + -5n

Reorder the terms:
13 + -9n + 8n2 = -11 + 11 + 5n + -5n

Combine like terms: -11 + 11 = 0
13 + -9n + 8n2 = 0 + 5n + -5n
13 + -9n + 8n2 = 5n + -5n

Combine like terms: 5n + -5n = 0
13 + -9n + 8n2 = 0

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

Divide each side by '8'.
1.625 + -1.125n + n2 = 0

Move the constant term to the right:

Add '-1.625' to each side of the equation.
1.625 + -1.125n + -1.625 + n2 = 0 + -1.625

Reorder the terms:
1.625 + -1.625 + -1.125n + n2 = 0 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + -1.125n + n2 = 0 + -1.625
-1.125n + n2 = 0 + -1.625

Combine like terms: 0 + -1.625 = -1.625
-1.125n + n2 = -1.625

The n term is -1.125n.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125n + 0.31640625 + n2 = -1.625 + 0.31640625

Reorder the terms:
0.31640625 + -1.125n + n2 = -1.625 + 0.31640625

Combine like terms: -1.625 + 0.31640625 = -1.30859375
0.31640625 + -1.125n + n2 = -1.30859375

Factor a perfect square on the left side:
(n + -0.5625)(n + -0.5625) = -1.30859375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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