u^2+6=2u^2-5u+37

Solution for u^2+6=2u^2-5u+37 equation:

Simplifying
u2 + 6 = 2u2 + -5u + 37

Reorder the terms:
6 + u2 = 2u2 + -5u + 37

Reorder the terms:
6 + u2 = 37 + -5u + 2u2

Solving
6 + u2 = 37 + -5u + 2u2

Solving for variable 'u'.

Reorder the terms:
6 + -37 + 5u + u2 + -2u2 = 37 + -5u + 2u2 + -37 + 5u + -2u2

Combine like terms: 6 + -37 = -31
-31 + 5u + u2 + -2u2 = 37 + -5u + 2u2 + -37 + 5u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-31 + 5u + -1u2 = 37 + -5u + 2u2 + -37 + 5u + -2u2

Reorder the terms:
-31 + 5u + -1u2 = 37 + -37 + -5u + 5u + 2u2 + -2u2

Combine like terms: 37 + -37 = 0
-31 + 5u + -1u2 = 0 + -5u + 5u + 2u2 + -2u2
-31 + 5u + -1u2 = -5u + 5u + 2u2 + -2u2

Combine like terms: -5u + 5u = 0
-31 + 5u + -1u2 = 0 + 2u2 + -2u2
-31 + 5u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-31 + 5u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
31 + -5u + u2 = 0

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -5u + -31 + u2 = 0 + -31

Reorder the terms:
31 + -31 + -5u + u2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -5u + u2 = 0 + -31
-5u + u2 = 0 + -31

Combine like terms: 0 + -31 = -31
-5u + u2 = -31

The u term is -5u.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5u + 6.25 + u2 = -31 + 6.25

Reorder the terms:
6.25 + -5u + u2 = -31 + 6.25

Combine like terms: -31 + 6.25 = -24.75
6.25 + -5u + u2 = -24.75

Factor a perfect square on the left side:
(u + -2.5)(u + -2.5) = -24.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.