u^2+u-21=0

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Solution for u^2+u-21=0 equation: 


Simplifying
u2 + u + -21 = 0

Reorder the terms:
-21 + u + u2 = 0

Solving
-21 + u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + u + 21 + u2 = 0 + 21

Reorder the terms:
-21 + 21 + u + u2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + u + u2 = 0 + 21
u + u2 = 0 + 21

Combine like terms: 0 + 21 = 21
u + u2 = 21

The u term is u.  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.
u + 0.25 + u2 = 21 + 0.25

Reorder the terms:
0.25 + u + u2 = 21 + 0.25

Combine like terms: 21 + 0.25 = 21.25
0.25 + u + u2 = 21.25

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(u + 0.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
u + 0.5 = 4.609772229

Simplifying
u + 0.5 = 4.609772229

Reorder the terms:
0.5 + u = 4.609772229

Solving
0.5 + u = 4.609772229

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 4.609772229 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 4.609772229 + -0.5
u = 4.609772229 + -0.5

Combine like terms: 4.609772229 + -0.5 = 4.109772229
u = 4.109772229

Simplifying
u = 4.109772229


Subproblem 2
u + 0.5 = -4.609772229

Simplifying
u + 0.5 = -4.609772229

Reorder the terms:
0.5 + u = -4.609772229

Solving
0.5 + u = -4.609772229

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -4.609772229 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -4.609772229 + -0.5
u = -4.609772229 + -0.5

Combine like terms: -4.609772229 + -0.5 = -5.109772229
u = -5.109772229

Simplifying
u = -5.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {4.109772229, -5.109772229}

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