0.074=(100-x)x

Solution for 0.074=(100-x)x equation:

Simplifying
0.074 = (100 + -1x) * x

Reorder the terms for easier multiplication:
0.074 = x(100 + -1x)
0.074 = (100 * x + -1x * x)
0.074 = (100x + -1x2)

Solving
0.074 = 100x + -1x2

Solving for variable 'x'.

Reorder the terms:
0.074 + -100x + x2 = 100x + -100x + -1x2 + x2

Combine like terms: 100x + -100x = 0
0.074 + -100x + x2 = 0 + -1x2 + x2
0.074 + -100x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
0.074 + -100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-0.074' to each side of the equation.
0.074 + -100x + -0.074 + x2 = 0 + -0.074

Reorder the terms:
0.074 + -0.074 + -100x + x2 = 0 + -0.074

Combine like terms: 0.074 + -0.074 = 0.000
0.000 + -100x + x2 = 0 + -0.074
-100x + x2 = 0 + -0.074

Combine like terms: 0 + -0.074 = -0.074
-100x + x2 = -0.074

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -0.074 + 2500

Reorder the terms:
2500 + -100x + x2 = -0.074 + 2500

Combine like terms: -0.074 + 2500 = 2499.926
2500 + -100x + x2 = 2499.926

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2499.926

Calculate the square root of the right side: 49.999259995

Break this problem into two subproblems by setting 
(x + -50) equal to 49.999259995 and -49.999259995.

Subproblem 1
x + -50 = 49.999259995

Simplifying
x + -50 = 49.999259995

Reorder the terms:
-50 + x = 49.999259995

Solving
-50 + x = 49.999259995

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = 49.999259995 + 50

Combine like terms: -50 + 50 = 0
0 + x = 49.999259995 + 50
x = 49.999259995 + 50

Combine like terms: 49.999259995 + 50 = 99.999259995
x = 99.999259995

Simplifying
x = 99.999259995

Subproblem 2
x + -50 = -49.999259995

Simplifying
x + -50 = -49.999259995

Reorder the terms:
-50 + x = -49.999259995

Solving
-50 + x = -49.999259995

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = -49.999259995 + 50

Combine like terms: -50 + 50 = 0
0 + x = -49.999259995 + 50
x = -49.999259995 + 50

Combine like terms: -49.999259995 + 50 = 0.000740005
x = 0.000740005

Simplifying
x = 0.000740005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {99.999259995, 0.000740005}