5+n(n+1)=2n

Solution for 5+n(n+1)=2n equation:

Simplifying
5 + n(n + 1) = 2n

Reorder the terms:
5 + n(1 + n) = 2n
5 + (1 * n + n * n) = 2n
5 + (1n + n2) = 2n

Solving
5 + 1n + n2 = 2n

Solving for variable 'n'.

Reorder the terms:
5 + 1n + -2n + n2 = 2n + -2n

Combine like terms: 1n + -2n = -1n
5 + -1n + n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
5 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -1n + -5 + n2 = 0 + -5

Reorder the terms:
5 + -5 + -1n + n2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n + n2 = 0 + -5
-1n + n2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1n + n2 = -5

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = -5 + 0.25

Reorder the terms:
0.25 + -1n + n2 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + -1n + n2 = -4.75

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.