-8n^2+5n+3=5

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Solution for -8n^2+5n+3=5 equation:


Simplifying
-8n2 + 5n + 3 = 5

Reorder the terms:
3 + 5n + -8n2 = 5

Solving
3 + 5n + -8n2 = 5

Solving for variable 'n'.

Reorder the terms:
3 + -5 + 5n + -8n2 = 5 + -5

Combine like terms: 3 + -5 = -2
-2 + 5n + -8n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-2 + 5n + -8n2 = 0

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

Divide each side by '-8'.
0.25 + -0.625n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.625n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.625n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.625n + n2 = 0 + -0.25
-0.625n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.625n + n2 = -0.25

The n term is -0.625n.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625n + 0.09765625 + n2 = -0.25 + 0.09765625

Reorder the terms:
0.09765625 + -0.625n + n2 = -0.25 + 0.09765625

Combine like terms: -0.25 + 0.09765625 = -0.15234375
0.09765625 + -0.625n + n2 = -0.15234375

Factor a perfect square on the left side:
(n + -0.3125)(n + -0.3125) = -0.15234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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