X^2+16X-3=0

Solution for X^2+16X-3=0 equation:

Simplifying
X2 + 16X + -3 = 0

Reorder the terms:
-3 + 16X + X2 = 0

Solving
-3 + 16X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 16X + 3 + X2 = 0 + 3

Reorder the terms:
-3 + 3 + 16X + X2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 16X + X2 = 0 + 3
16X + X2 = 0 + 3

Combine like terms: 0 + 3 = 3
16X + X2 = 3

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 = 3 + 64

Reorder the terms:
64 + 16X + X2 = 3 + 64

Combine like terms: 3 + 64 = 67
64 + 16X + X2 = 67

Factor a perfect square on the left side:
(X + 8)(X + 8) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(X + 8) equal to 8.185352772 and -8.185352772.

Subproblem 1
X + 8 = 8.185352772

Simplifying
X + 8 = 8.185352772

Reorder the terms:
8 + X = 8.185352772

Solving
8 + X = 8.185352772

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 = 8.185352772 + -8

Combine like terms: 8 + -8 = 0
0 + X = 8.185352772 + -8
X = 8.185352772 + -8

Combine like terms: 8.185352772 + -8 = 0.185352772
X = 0.185352772

Simplifying
X = 0.185352772

Subproblem 2
X + 8 = -8.185352772

Simplifying
X + 8 = -8.185352772

Reorder the terms:
8 + X = -8.185352772

Solving
8 + X = -8.185352772

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 = -8.185352772 + -8

Combine like terms: 8 + -8 = 0
0 + X = -8.185352772 + -8
X = -8.185352772 + -8

Combine like terms: -8.185352772 + -8 = -16.185352772
X = -16.185352772

Simplifying
X = -16.185352772

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.185352772, -16.185352772}