2x(x-8)=20

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Solution for 2x(x-8)=20 equation: 


Simplifying
2x(x + -8) = 20

Reorder the terms:
2x(-8 + x) = 20
(-8 * 2x + x * 2x) = 20
(-16x + 2x2) = 20

Solving
-16x + 2x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -16x + 2x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + -8x + x2 = 0

Solving
-10 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -8x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -8x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -8x + x2 = 0 + 10
-8x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-8x + x2 = 10

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 = 10 + 16

Reorder the terms:
16 + -8x + x2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + -8x + x2 = 26

Factor a perfect square on the left side:
(x + -4)(x + -4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -4) equal to 5.099019514 and -5.099019514.


Subproblem 1
x + -4 = 5.099019514

Simplifying
x + -4 = 5.099019514

Reorder the terms:
-4 + x = 5.099019514

Solving
-4 + x = 5.099019514

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 = 5.099019514 + 4

Combine like terms: -4 + 4 = 0
0 + x = 5.099019514 + 4
x = 5.099019514 + 4

Combine like terms: 5.099019514 + 4 = 9.099019514
x = 9.099019514

Simplifying
x = 9.099019514


Subproblem 2
x + -4 = -5.099019514

Simplifying
x + -4 = -5.099019514

Reorder the terms:
-4 + x = -5.099019514

Solving
-4 + x = -5.099019514

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 = -5.099019514 + 4

Combine like terms: -4 + 4 = 0
0 + x = -5.099019514 + 4
x = -5.099019514 + 4

Combine like terms: -5.099019514 + 4 = -1.099019514
x = -1.099019514

Simplifying
x = -1.099019514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.099019514, -1.099019514}
Solution
x = {9.099019514, -1.099019514}

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