t^2+16t-200=0

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


Simplifying
t2 + 16t + -200 = 0

Reorder the terms:
-200 + 16t + t2 = 0

Solving
-200 + 16t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 16t + 200 + t2 = 0 + 200

Reorder the terms:
-200 + 200 + 16t + t2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 16t + t2 = 0 + 200
16t + t2 = 0 + 200

Combine like terms: 0 + 200 = 200
16t + t2 = 200

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

Add '64' to each side of the equation.
16t + 64 + t2 = 200 + 64

Reorder the terms:
64 + 16t + t2 = 200 + 64

Combine like terms: 200 + 64 = 264
64 + 16t + t2 = 264

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

Calculate the square root of the right side: 16.248076809

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


Subproblem 1
t + 8 = 16.248076809

Simplifying
t + 8 = 16.248076809

Reorder the terms:
8 + t = 16.248076809

Solving
8 + t = 16.248076809

Solving for variable 't'.

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

Add '-8' to each side of the equation.
8 + -8 + t = 16.248076809 + -8

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

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

Simplifying
t = 8.248076809


Subproblem 2
t + 8 = -16.248076809

Simplifying
t + 8 = -16.248076809

Reorder the terms:
8 + t = -16.248076809

Solving
8 + t = -16.248076809

Solving for variable 't'.

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

Add '-8' to each side of the equation.
8 + -8 + t = -16.248076809 + -8

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

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

Simplifying
t = -24.248076809


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

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