25*(36+x^2)=16*(200-40*x-x^2)

Solution for 25*(36+x^2)=16*(200-40*x-x^2) equation:

Simplifying
25(36 + x2) = 16(200 + -40x + -1x2)
(36 * 25 + x2 * 25) = 16(200 + -40x + -1x2)
(900 + 25x2) = 16(200 + -40x + -1x2)
900 + 25x2 = (200 * 16 + -40x * 16 + -1x2 * 16)
900 + 25x2 = (3200 + -640x + -16x2)

Solving
900 + 25x2 = 3200 + -640x + -16x2

Solving for variable 'x'.

Reorder the terms:
900 + -3200 + 640x + 25x2 + 16x2 = 3200 + -640x + -16x2 + -3200 + 640x + 16x2

Combine like terms: 900 + -3200 = -2300
-2300 + 640x + 25x2 + 16x2 = 3200 + -640x + -16x2 + -3200 + 640x + 16x2

Combine like terms: 25x2 + 16x2 = 41x2
-2300 + 640x + 41x2 = 3200 + -640x + -16x2 + -3200 + 640x + 16x2

Reorder the terms:
-2300 + 640x + 41x2 = 3200 + -3200 + -640x + 640x + -16x2 + 16x2

Combine like terms: 3200 + -3200 = 0
-2300 + 640x + 41x2 = 0 + -640x + 640x + -16x2 + 16x2
-2300 + 640x + 41x2 = -640x + 640x + -16x2 + 16x2

Combine like terms: -640x + 640x = 0
-2300 + 640x + 41x2 = 0 + -16x2 + 16x2
-2300 + 640x + 41x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-2300 + 640x + 41x2 = 0

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

Divide each side by '41'.
-56.09756098 + 15.6097561x + x2 = 0

Move the constant term to the right:

Add '56.09756098' to each side of the equation.
-56.09756098 + 15.6097561x + 56.09756098 + x2 = 0 + 56.09756098

Reorder the terms:
-56.09756098 + 56.09756098 + 15.6097561x + x2 = 0 + 56.09756098

Combine like terms: -56.09756098 + 56.09756098 = 0.00000000
0.00000000 + 15.6097561x + x2 = 0 + 56.09756098
15.6097561x + x2 = 0 + 56.09756098

Combine like terms: 0 + 56.09756098 = 56.09756098
15.6097561x + x2 = 56.09756098

The x term is 15.6097561x.  Take half its coefficient (7.80487805).
Square it (60.91612138) and add it to both sides.

Add '60.91612138' to each side of the equation.
15.6097561x + 60.91612138 + x2 = 56.09756098 + 60.91612138

Reorder the terms:
60.91612138 + 15.6097561x + x2 = 56.09756098 + 60.91612138

Combine like terms: 56.09756098 + 60.91612138 = 117.01368236
60.91612138 + 15.6097561x + x2 = 117.01368236

Factor a perfect square on the left side:
(x + 7.80487805)(x + 7.80487805) = 117.01368236

Calculate the square root of the right side: 10.817286275

Break this problem into two subproblems by setting 
(x + 7.80487805) equal to 10.817286275 and -10.817286275.

Subproblem 1
x + 7.80487805 = 10.817286275

Simplifying
x + 7.80487805 = 10.817286275

Reorder the terms:
7.80487805 + x = 10.817286275

Solving
7.80487805 + x = 10.817286275

Solving for variable 'x'.

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

Add '-7.80487805' to each side of the equation.
7.80487805 + -7.80487805 + x = 10.817286275 + -7.80487805

Combine like terms: 7.80487805 + -7.80487805 = 0.00000000
0.00000000 + x = 10.817286275 + -7.80487805
x = 10.817286275 + -7.80487805

Combine like terms: 10.817286275 + -7.80487805 = 3.012408225
x = 3.012408225

Simplifying
x = 3.012408225

Subproblem 2
x + 7.80487805 = -10.817286275

Simplifying
x + 7.80487805 = -10.817286275

Reorder the terms:
7.80487805 + x = -10.817286275

Solving
7.80487805 + x = -10.817286275

Solving for variable 'x'.

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

Add '-7.80487805' to each side of the equation.
7.80487805 + -7.80487805 + x = -10.817286275 + -7.80487805

Combine like terms: 7.80487805 + -7.80487805 = 0.00000000
0.00000000 + x = -10.817286275 + -7.80487805
x = -10.817286275 + -7.80487805

Combine like terms: -10.817286275 + -7.80487805 = -18.622164325
x = -18.622164325

Simplifying
x = -18.622164325

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.012408225, -18.622164325}