4u^2+21u-20=0

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Solution for 4u^2+21u-20=0 equation: 


Simplifying
4u2 + 21u + -20 = 0

Reorder the terms:
-20 + 21u + 4u2 = 0

Solving
-20 + 21u + 4u2 = 0

Solving for variable 'u'.

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

Divide each side by '4'.
-5 + 5.25u + u2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 5.25u + 5 + u2 = 0 + 5

Reorder the terms:
-5 + 5 + 5.25u + u2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 5.25u + u2 = 0 + 5
5.25u + u2 = 0 + 5

Combine like terms: 0 + 5 = 5
5.25u + u2 = 5

The u term is 5.25u.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25u + 6.890625 + u2 = 5 + 6.890625

Reorder the terms:
6.890625 + 5.25u + u2 = 5 + 6.890625

Combine like terms: 5 + 6.890625 = 11.890625
6.890625 + 5.25u + u2 = 11.890625

Factor a perfect square on the left side:
(u + 2.625)(u + 2.625) = 11.890625

Calculate the square root of the right side: 3.448278556

Break this problem into two subproblems by setting 
(u + 2.625) equal to 3.448278556 and -3.448278556.


Subproblem 1
u + 2.625 = 3.448278556

Simplifying
u + 2.625 = 3.448278556

Reorder the terms:
2.625 + u = 3.448278556

Solving
2.625 + u = 3.448278556

Solving for variable 'u'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + u = 3.448278556 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + u = 3.448278556 + -2.625
u = 3.448278556 + -2.625

Combine like terms: 3.448278556 + -2.625 = 0.823278556
u = 0.823278556

Simplifying
u = 0.823278556


Subproblem 2
u + 2.625 = -3.448278556

Simplifying
u + 2.625 = -3.448278556

Reorder the terms:
2.625 + u = -3.448278556

Solving
2.625 + u = -3.448278556

Solving for variable 'u'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + u = -3.448278556 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + u = -3.448278556 + -2.625
u = -3.448278556 + -2.625

Combine like terms: -3.448278556 + -2.625 = -6.073278556
u = -6.073278556

Simplifying
u = -6.073278556


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.823278556, -6.073278556}

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