4n^2-7n+22=0

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Solution for 4n^2-7n+22=0 equation:


Simplifying
4n2 + -7n + 22 = 0

Reorder the terms:
22 + -7n + 4n2 = 0

Solving
22 + -7n + 4n2 = 0

Solving for variable 'n'.

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

Divide each side by '4'.
5.5 + -1.75n + n2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -1.75n + -5.5 + n2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -1.75n + n2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -1.75n + n2 = 0 + -5.5
-1.75n + n2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-1.75n + n2 = -5.5

The n term is -1.75n.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75n + 0.765625 + n2 = -5.5 + 0.765625

Reorder the terms:
0.765625 + -1.75n + n2 = -5.5 + 0.765625

Combine like terms: -5.5 + 0.765625 = -4.734375
0.765625 + -1.75n + n2 = -4.734375

Factor a perfect square on the left side:
(n + -0.875)(n + -0.875) = -4.734375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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