(2x-20)(x)=5400

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Solution for (2x-20)(x)=5400 equation: 


Simplifying
(2x + -20)(x) = 5400

Reorder the terms:
(-20 + 2x)(x) = 5400

Reorder the terms for easier multiplication:
x(-20 + 2x) = 5400
(-20 * x + 2x * x) = 5400
(-20x + 2x2) = 5400

Solving
-20x + 2x2 = 5400

Solving for variable 'x'.

Reorder the terms:
-5400 + -20x + 2x2 = 5400 + -5400

Combine like terms: 5400 + -5400 = 0
-5400 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2700 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2700 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-2700 + -10x + x2 = 0

Solving
-2700 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2700' to each side of the equation.
-2700 + -10x + 2700 + x2 = 0 + 2700

Reorder the terms:
-2700 + 2700 + -10x + x2 = 0 + 2700

Combine like terms: -2700 + 2700 = 0
0 + -10x + x2 = 0 + 2700
-10x + x2 = 0 + 2700

Combine like terms: 0 + 2700 = 2700
-10x + x2 = 2700

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 = 2700 + 25

Reorder the terms:
25 + -10x + x2 = 2700 + 25

Combine like terms: 2700 + 25 = 2725
25 + -10x + x2 = 2725

Factor a perfect square on the left side:
(x + -5)(x + -5) = 2725

Calculate the square root of the right side: 52.201532545

Break this problem into two subproblems by setting 
(x + -5) equal to 52.201532545 and -52.201532545.


Subproblem 1
x + -5 = 52.201532545

Simplifying
x + -5 = 52.201532545

Reorder the terms:
-5 + x = 52.201532545

Solving
-5 + x = 52.201532545

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 = 52.201532545 + 5

Combine like terms: -5 + 5 = 0
0 + x = 52.201532545 + 5
x = 52.201532545 + 5

Combine like terms: 52.201532545 + 5 = 57.201532545
x = 57.201532545

Simplifying
x = 57.201532545


Subproblem 2
x + -5 = -52.201532545

Simplifying
x + -5 = -52.201532545

Reorder the terms:
-5 + x = -52.201532545

Solving
-5 + x = -52.201532545

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 = -52.201532545 + 5

Combine like terms: -5 + 5 = 0
0 + x = -52.201532545 + 5
x = -52.201532545 + 5

Combine like terms: -52.201532545 + 5 = -47.201532545
x = -47.201532545

Simplifying
x = -47.201532545


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {57.201532545, -47.201532545}
Solution
x = {57.201532545, -47.201532545}

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