x^2+16x-2100=0

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Solution for x^2+16x-2100=0 equation: 


Simplifying
x2 + 16x + -2100 = 0

Reorder the terms:
-2100 + 16x + x2 = 0

Solving
-2100 + 16x + 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 + 16x + 2100 + x2 = 0 + 2100

Reorder the terms:
-2100 + 2100 + 16x + x2 = 0 + 2100

Combine like terms: -2100 + 2100 = 0
0 + 16x + x2 = 0 + 2100
16x + x2 = 0 + 2100

Combine like terms: 0 + 2100 = 2100
16x + x2 = 2100

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 2100 + 64

Reorder the terms:
64 + 16x + x2 = 2100 + 64

Combine like terms: 2100 + 64 = 2164
64 + 16x + x2 = 2164

Factor a perfect square on the left side:
(x + 8)(x + 8) = 2164

Calculate the square root of the right side: 46.518813398

Break this problem into two subproblems by setting 
(x + 8) equal to 46.518813398 and -46.518813398.


Subproblem 1
x + 8 = 46.518813398

Simplifying
x + 8 = 46.518813398

Reorder the terms:
8 + x = 46.518813398

Solving
8 + x = 46.518813398

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 46.518813398 + -8

Combine like terms: 8 + -8 = 0
0 + x = 46.518813398 + -8
x = 46.518813398 + -8

Combine like terms: 46.518813398 + -8 = 38.518813398
x = 38.518813398

Simplifying
x = 38.518813398


Subproblem 2
x + 8 = -46.518813398

Simplifying
x + 8 = -46.518813398

Reorder the terms:
8 + x = -46.518813398

Solving
8 + x = -46.518813398

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -46.518813398 + -8

Combine like terms: 8 + -8 = 0
0 + x = -46.518813398 + -8
x = -46.518813398 + -8

Combine like terms: -46.518813398 + -8 = -54.518813398
x = -54.518813398

Simplifying
x = -54.518813398


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.518813398, -54.518813398}

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