4x(25-4x)=25

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Solution for 4x(25-4x)=25 equation: 


Simplifying
4x(25 + -4x) = 25
(25 * 4x + -4x * 4x) = 25
(100x + -16x2) = 25

Solving
100x + -16x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 100x + -16x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 100x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
1.5625 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-1.5625' to each side of the equation.
1.5625 + -6.25x + -1.5625 + x2 = 0 + -1.5625

Reorder the terms:
1.5625 + -1.5625 + -6.25x + x2 = 0 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + -6.25x + x2 = 0 + -1.5625
-6.25x + x2 = 0 + -1.5625

Combine like terms: 0 + -1.5625 = -1.5625
-6.25x + x2 = -1.5625

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -1.5625 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -1.5625 + 9.765625

Combine like terms: -1.5625 + 9.765625 = 8.203125
9.765625 + -6.25x + x2 = 8.203125

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 8.203125

Calculate the square root of the right side: 2.864109809

Break this problem into two subproblems by setting 
(x + -3.125) equal to 2.864109809 and -2.864109809.


Subproblem 1
x + -3.125 = 2.864109809

Simplifying
x + -3.125 = 2.864109809

Reorder the terms:
-3.125 + x = 2.864109809

Solving
-3.125 + x = 2.864109809

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 2.864109809 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 2.864109809 + 3.125
x = 2.864109809 + 3.125

Combine like terms: 2.864109809 + 3.125 = 5.989109809
x = 5.989109809

Simplifying
x = 5.989109809


Subproblem 2
x + -3.125 = -2.864109809

Simplifying
x + -3.125 = -2.864109809

Reorder the terms:
-3.125 + x = -2.864109809

Solving
-3.125 + x = -2.864109809

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -2.864109809 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -2.864109809 + 3.125
x = -2.864109809 + 3.125

Combine like terms: -2.864109809 + 3.125 = 0.260890191
x = 0.260890191

Simplifying
x = 0.260890191


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.989109809, 0.260890191}

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