4x^2-40x+20=0

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Solution for 4x^2-40x+20=0 equation: 


Simplifying
4x2 + -40x + 20 = 0

Reorder the terms:
20 + -40x + 4x2 = 0

Solving
20 + -40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -10x + x2 = 0

Solving
5 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -10x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10x + x2 = 0 + -5
-10x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-10x + x2 = -5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -5 + 25

Reorder the terms:
25 + -10x + x2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + -10x + x2 = 20

Factor a perfect square on the left side:
(x + -5)(x + -5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -5) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + -5 = 4.472135955

Simplifying
x + -5 = 4.472135955

Reorder the terms:
-5 + x = 4.472135955

Solving
-5 + x = 4.472135955

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.472135955 + 5
x = 4.472135955 + 5

Combine like terms: 4.472135955 + 5 = 9.472135955
x = 9.472135955

Simplifying
x = 9.472135955


Subproblem 2
x + -5 = -4.472135955

Simplifying
x + -5 = -4.472135955

Reorder the terms:
-5 + x = -4.472135955

Solving
-5 + x = -4.472135955

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.472135955 + 5
x = -4.472135955 + 5

Combine like terms: -4.472135955 + 5 = 0.527864045
x = 0.527864045

Simplifying
x = 0.527864045


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.472135955, 0.527864045}
Solution
x = {9.472135955, 0.527864045}

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