5x(5-x)=-30x+25

Solution for 5x(5-x)=-30x+25 equation:

Simplifying
5x(5 + -1x) = -30x + 25
(5 * 5x + -1x * 5x) = -30x + 25
(25x + -5x2) = -30x + 25

Reorder the terms:
25x + -5x2 = 25 + -30x

Solving
25x + -5x2 = 25 + -30x

Solving for variable 'x'.

Reorder the terms:
-25 + 25x + 30x + -5x2 = 25 + -30x + -25 + 30x

Combine like terms: 25x + 30x = 55x
-25 + 55x + -5x2 = 25 + -30x + -25 + 30x

Reorder the terms:
-25 + 55x + -5x2 = 25 + -25 + -30x + 30x

Combine like terms: 25 + -25 = 0
-25 + 55x + -5x2 = 0 + -30x + 30x
-25 + 55x + -5x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-25 + 55x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 11x + -1x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-5 + 11x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 11x + -1x2 = 0

Solving
-5 + 11x + -1x2 = 0

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

Divide each side by '-1'.
5 + -11x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -11x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -11x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -11x + x2 = 0 + -5
-11x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-11x + x2 = -5

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -5 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -5 + 30.25

Combine like terms: -5 + 30.25 = 25.25
30.25 + -11x + x2 = 25.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.024937811 and -5.024937811.

Subproblem 1
x + -5.5 = 5.024937811

Simplifying
x + -5.5 = 5.024937811

Reorder the terms:
-5.5 + x = 5.024937811

Solving
-5.5 + x = 5.024937811

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.024937811 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.024937811 + 5.5
x = 5.024937811 + 5.5

Combine like terms: 5.024937811 + 5.5 = 10.524937811
x = 10.524937811

Simplifying
x = 10.524937811

Subproblem 2
x + -5.5 = -5.024937811

Simplifying
x + -5.5 = -5.024937811

Reorder the terms:
-5.5 + x = -5.024937811

Solving
-5.5 + x = -5.024937811

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.024937811 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.024937811 + 5.5
x = -5.024937811 + 5.5

Combine like terms: -5.024937811 + 5.5 = 0.475062189
x = 0.475062189

Simplifying
x = 0.475062189

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.524937811, 0.475062189}
Solution
x = {10.524937811, 0.475062189}