-4x^2+41x-20=0

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Solution for -4x^2+41x-20=0 equation: 


Simplifying
-4x2 + 41x + -20 = 0

Reorder the terms:
-20 + 41x + -4x2 = 0

Solving
-20 + 41x + -4x2 = 0

Solving for variable 'x'.

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

Divide each side by '-4'.
5 + -10.25x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10.25x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -10.25x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10.25x + x2 = 0 + -5
-10.25x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-10.25x + x2 = -5

The x term is -10.25x.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25x + 26.265625 + x2 = -5 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = -5 + 26.265625

Combine like terms: -5 + 26.265625 = 21.265625
26.265625 + -10.25x + x2 = 21.265625

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = 21.265625

Calculate the square root of the right side: 4.611466686

Break this problem into two subproblems by setting 
(x + -5.125) equal to 4.611466686 and -4.611466686.


Subproblem 1
x + -5.125 = 4.611466686

Simplifying
x + -5.125 = 4.611466686

Reorder the terms:
-5.125 + x = 4.611466686

Solving
-5.125 + x = 4.611466686

Solving for variable 'x'.

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

Add '5.125' to each side of the equation.
-5.125 + 5.125 + x = 4.611466686 + 5.125

Combine like terms: -5.125 + 5.125 = 0.000
0.000 + x = 4.611466686 + 5.125
x = 4.611466686 + 5.125

Combine like terms: 4.611466686 + 5.125 = 9.736466686
x = 9.736466686

Simplifying
x = 9.736466686


Subproblem 2
x + -5.125 = -4.611466686

Simplifying
x + -5.125 = -4.611466686

Reorder the terms:
-5.125 + x = -4.611466686

Solving
-5.125 + x = -4.611466686

Solving for variable 'x'.

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

Add '5.125' to each side of the equation.
-5.125 + 5.125 + x = -4.611466686 + 5.125

Combine like terms: -5.125 + 5.125 = 0.000
0.000 + x = -4.611466686 + 5.125
x = -4.611466686 + 5.125

Combine like terms: -4.611466686 + 5.125 = 0.513533314
x = 0.513533314

Simplifying
x = 0.513533314


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.736466686, 0.513533314}

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