x^2-96x+2100=0

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Solution for x^2-96x+2100=0 equation: 


Simplifying
x2 + -96x + 2100 = 0

Reorder the terms:
2100 + -96x + x2 = 0

Solving
2100 + -96x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2100' to each side of the equation.
2100 + -96x + -2100 + x2 = 0 + -2100

Reorder the terms:
2100 + -2100 + -96x + x2 = 0 + -2100

Combine like terms: 2100 + -2100 = 0
0 + -96x + x2 = 0 + -2100
-96x + x2 = 0 + -2100

Combine like terms: 0 + -2100 = -2100
-96x + x2 = -2100

The x term is -96x.  Take half its coefficient (-48).
Square it (2304) and add it to both sides.

Add '2304' to each side of the equation.
-96x + 2304 + x2 = -2100 + 2304

Reorder the terms:
2304 + -96x + x2 = -2100 + 2304

Combine like terms: -2100 + 2304 = 204
2304 + -96x + x2 = 204

Factor a perfect square on the left side:
(x + -48)(x + -48) = 204

Calculate the square root of the right side: 14.282856857

Break this problem into two subproblems by setting 
(x + -48) equal to 14.282856857 and -14.282856857.


Subproblem 1
x + -48 = 14.282856857

Simplifying
x + -48 = 14.282856857

Reorder the terms:
-48 + x = 14.282856857

Solving
-48 + x = 14.282856857

Solving for variable 'x'.

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

Add '48' to each side of the equation.
-48 + 48 + x = 14.282856857 + 48

Combine like terms: -48 + 48 = 0
0 + x = 14.282856857 + 48
x = 14.282856857 + 48

Combine like terms: 14.282856857 + 48 = 62.282856857
x = 62.282856857

Simplifying
x = 62.282856857


Subproblem 2
x + -48 = -14.282856857

Simplifying
x + -48 = -14.282856857

Reorder the terms:
-48 + x = -14.282856857

Solving
-48 + x = -14.282856857

Solving for variable 'x'.

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

Add '48' to each side of the equation.
-48 + 48 + x = -14.282856857 + 48

Combine like terms: -48 + 48 = 0
0 + x = -14.282856857 + 48
x = -14.282856857 + 48

Combine like terms: -14.282856857 + 48 = 33.717143143
x = 33.717143143

Simplifying
x = 33.717143143


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {62.282856857, 33.717143143}

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