x^2+16x-200=0

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Solution for x^2+16x-200=0 equation: 


Simplifying
x2 + 16x + -200 = 0

Reorder the terms:
-200 + 16x + x2 = 0

Solving
-200 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 16x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 16x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 16x + x2 = 0 + 200
16x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
16x + x2 = 200

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 = 200 + 64

Reorder the terms:
64 + 16x + x2 = 200 + 64

Combine like terms: 200 + 64 = 264
64 + 16x + x2 = 264

Factor a perfect square on the left side:
(x + 8)(x + 8) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(x + 8) equal to 16.248076809 and -16.248076809.


Subproblem 1
x + 8 = 16.248076809

Simplifying
x + 8 = 16.248076809

Reorder the terms:
8 + x = 16.248076809

Solving
8 + x = 16.248076809

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 = 16.248076809 + -8

Combine like terms: 8 + -8 = 0
0 + x = 16.248076809 + -8
x = 16.248076809 + -8

Combine like terms: 16.248076809 + -8 = 8.248076809
x = 8.248076809

Simplifying
x = 8.248076809


Subproblem 2
x + 8 = -16.248076809

Simplifying
x + 8 = -16.248076809

Reorder the terms:
8 + x = -16.248076809

Solving
8 + x = -16.248076809

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 = -16.248076809 + -8

Combine like terms: 8 + -8 = 0
0 + x = -16.248076809 + -8
x = -16.248076809 + -8

Combine like terms: -16.248076809 + -8 = -24.248076809
x = -24.248076809

Simplifying
x = -24.248076809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.248076809, -24.248076809}

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