(2x-4)*x=100

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Solution for (2x-4)*x=100 equation: 


Simplifying
(2x + -4) * x = 100

Reorder the terms:
(-4 + 2x) * x = 100

Reorder the terms for easier multiplication:
x(-4 + 2x) = 100
(-4 * x + 2x * x) = 100
(-4x + 2x2) = 100

Solving
-4x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -4x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + -2x + x2 = 0

Solving
-50 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -2x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -2x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -2x + x2 = 0 + 50
-2x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-2x + x2 = 50

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 50 + 1

Reorder the terms:
1 + -2x + x2 = 50 + 1

Combine like terms: 50 + 1 = 51
1 + -2x + x2 = 51

Factor a perfect square on the left side:
(x + -1)(x + -1) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -1) equal to 7.141428429 and -7.141428429.


Subproblem 1
x + -1 = 7.141428429

Simplifying
x + -1 = 7.141428429

Reorder the terms:
-1 + x = 7.141428429

Solving
-1 + x = 7.141428429

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 7.141428429 + 1

Combine like terms: -1 + 1 = 0
0 + x = 7.141428429 + 1
x = 7.141428429 + 1

Combine like terms: 7.141428429 + 1 = 8.141428429
x = 8.141428429

Simplifying
x = 8.141428429


Subproblem 2
x + -1 = -7.141428429

Simplifying
x + -1 = -7.141428429

Reorder the terms:
-1 + x = -7.141428429

Solving
-1 + x = -7.141428429

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -7.141428429 + 1

Combine like terms: -1 + 1 = 0
0 + x = -7.141428429 + 1
x = -7.141428429 + 1

Combine like terms: -7.141428429 + 1 = -6.141428429
x = -6.141428429

Simplifying
x = -6.141428429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.141428429, -6.141428429}
Solution
x = {8.141428429, -6.141428429}

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