4x^2-32x+20=0

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Solution for 4x^2-32x+20=0 equation: 


Simplifying
4x2 + -32x + 20 = 0

Reorder the terms:
20 + -32x + 4x2 = 0

Solving
20 + -32x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -8x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -8x + x2 = 0

Solving
5 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x + x2 = 0 + -5
-8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8x + x2 = -5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -5 + 16

Reorder the terms:
16 + -8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8x + x2 = 11

Factor a perfect square on the left side:
(x + -4)(x + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -4) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + -4 = 3.31662479

Simplifying
x + -4 = 3.31662479

Reorder the terms:
-4 + x = 3.31662479

Solving
-4 + x = 3.31662479

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.31662479 + 4
x = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
x = 7.31662479

Simplifying
x = 7.31662479


Subproblem 2
x + -4 = -3.31662479

Simplifying
x + -4 = -3.31662479

Reorder the terms:
-4 + x = -3.31662479

Solving
-4 + x = -3.31662479

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.31662479 + 4
x = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
x = 0.68337521

Simplifying
x = 0.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.31662479, 0.68337521}
Solution
x = {7.31662479, 0.68337521}

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