x(80-2x)=700

Solution for x(80-2x)=700 equation:

Simplifying
x(80 + -2x) = 700
(80 * x + -2x * x) = 700
(80x + -2x2) = 700

Solving
80x + -2x2 = 700

Solving for variable 'x'.

Reorder the terms:
-700 + 80x + -2x2 = 700 + -700

Combine like terms: 700 + -700 = 0
-700 + 80x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-350 + 40x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-350 + 40x + -1x2)' equal to zero and attempt to solve:

Simplifying
-350 + 40x + -1x2 = 0

Solving
-350 + 40x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
350 + -40x + x2 = 0

Move the constant term to the right:

Add '-350' to each side of the equation.
350 + -40x + -350 + x2 = 0 + -350

Reorder the terms:
350 + -350 + -40x + x2 = 0 + -350

Combine like terms: 350 + -350 = 0
0 + -40x + x2 = 0 + -350
-40x + x2 = 0 + -350

Combine like terms: 0 + -350 = -350
-40x + x2 = -350

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -350 + 400

Reorder the terms:
400 + -40x + x2 = -350 + 400

Combine like terms: -350 + 400 = 50
400 + -40x + x2 = 50

Factor a perfect square on the left side:
(x + -20)(x + -20) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + -20) equal to 7.071067812 and -7.071067812.

Subproblem 1
x + -20 = 7.071067812

Simplifying
x + -20 = 7.071067812

Reorder the terms:
-20 + x = 7.071067812

Solving
-20 + x = 7.071067812

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 7.071067812 + 20

Combine like terms: -20 + 20 = 0
0 + x = 7.071067812 + 20
x = 7.071067812 + 20

Combine like terms: 7.071067812 + 20 = 27.071067812
x = 27.071067812

Simplifying
x = 27.071067812

Subproblem 2
x + -20 = -7.071067812

Simplifying
x + -20 = -7.071067812

Reorder the terms:
-20 + x = -7.071067812

Solving
-20 + x = -7.071067812

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -7.071067812 + 20

Combine like terms: -20 + 20 = 0
0 + x = -7.071067812 + 20
x = -7.071067812 + 20

Combine like terms: -7.071067812 + 20 = 12.928932188
x = 12.928932188

Simplifying
x = 12.928932188

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.071067812, 12.928932188}
Solution
x = {27.071067812, 12.928932188}