100x=(x^2+81)

Solution for 100x=(x^2+81) equation:

Simplifying
100x = (x2 + 81)

Reorder the terms:
100x = (81 + x2)

Remove parenthesis around (81 + x2)
100x = 81 + x2

Solving
100x = 81 + x2

Solving for variable 'x'.

Reorder the terms:
-81 + 100x + -1x2 = 81 + x2 + -81 + -1x2

Reorder the terms:
-81 + 100x + -1x2 = 81 + -81 + x2 + -1x2

Combine like terms: 81 + -81 = 0
-81 + 100x + -1x2 = 0 + x2 + -1x2
-81 + 100x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-81 + 100x + -1x2 = 0

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

Divide each side by '-1'.
81 + -100x + x2 = 0

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + -100x + -81 + x2 = 0 + -81

Reorder the terms:
81 + -81 + -100x + x2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -100x + x2 = 0 + -81
-100x + x2 = 0 + -81

Combine like terms: 0 + -81 = -81
-100x + x2 = -81

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 = -81 + 2500

Reorder the terms:
2500 + -100x + x2 = -81 + 2500

Combine like terms: -81 + 2500 = 2419
2500 + -100x + x2 = 2419

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2419

Calculate the square root of the right side: 49.183330509

Break this problem into two subproblems by setting 
(x + -50) equal to 49.183330509 and -49.183330509.

Subproblem 1
x + -50 = 49.183330509

Simplifying
x + -50 = 49.183330509

Reorder the terms:
-50 + x = 49.183330509

Solving
-50 + x = 49.183330509

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 = 49.183330509 + 50

Combine like terms: -50 + 50 = 0
0 + x = 49.183330509 + 50
x = 49.183330509 + 50

Combine like terms: 49.183330509 + 50 = 99.183330509
x = 99.183330509

Simplifying
x = 99.183330509

Subproblem 2
x + -50 = -49.183330509

Simplifying
x + -50 = -49.183330509

Reorder the terms:
-50 + x = -49.183330509

Solving
-50 + x = -49.183330509

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 = -49.183330509 + 50

Combine like terms: -50 + 50 = 0
0 + x = -49.183330509 + 50
x = -49.183330509 + 50

Combine like terms: -49.183330509 + 50 = 0.816669491
x = 0.816669491

Simplifying
x = 0.816669491

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {99.183330509, 0.816669491}