u^2-9u+15=0

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Solution for u^2-9u+15=0 equation: 


Simplifying
u2 + -9u + 15 = 0

Reorder the terms:
15 + -9u + u2 = 0

Solving
15 + -9u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -9u + -15 + u2 = 0 + -15

Reorder the terms:
15 + -15 + -9u + u2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -9u + u2 = 0 + -15
-9u + u2 = 0 + -15

Combine like terms: 0 + -15 = -15
-9u + u2 = -15

The u term is -9u.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9u + 20.25 + u2 = -15 + 20.25

Reorder the terms:
20.25 + -9u + u2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + -9u + u2 = 5.25

Factor a perfect square on the left side:
(u + -4.5)(u + -4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(u + -4.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
u + -4.5 = 2.291287847

Simplifying
u + -4.5 = 2.291287847

Reorder the terms:
-4.5 + u = 2.291287847

Solving
-4.5 + u = 2.291287847

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '4.5' to each side of the equation.
-4.5 + 4.5 + u = 2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + u = 2.291287847 + 4.5
u = 2.291287847 + 4.5

Combine like terms: 2.291287847 + 4.5 = 6.791287847
u = 6.791287847

Simplifying
u = 6.791287847


Subproblem 2
u + -4.5 = -2.291287847

Simplifying
u + -4.5 = -2.291287847

Reorder the terms:
-4.5 + u = -2.291287847

Solving
-4.5 + u = -2.291287847

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '4.5' to each side of the equation.
-4.5 + 4.5 + u = -2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + u = -2.291287847 + 4.5
u = -2.291287847 + 4.5

Combine like terms: -2.291287847 + 4.5 = 2.208712153
u = 2.208712153

Simplifying
u = 2.208712153


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {6.791287847, 2.208712153}

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