8x^2+16x-194=0

Solution for 8x^2+16x-194=0 equation:

Simplifying
8x2 + 16x + -194 = 0

Reorder the terms:
-194 + 16x + 8x2 = 0

Solving
-194 + 16x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-97 + 8x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-97 + 8x + 4x2)' equal to zero and attempt to solve:

Simplifying
-97 + 8x + 4x2 = 0

Solving
-97 + 8x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-24.25 + 2x + x2 = 0

Move the constant term to the right:

Add '24.25' to each side of the equation.
-24.25 + 2x + 24.25 + x2 = 0 + 24.25

Reorder the terms:
-24.25 + 24.25 + 2x + x2 = 0 + 24.25

Combine like terms: -24.25 + 24.25 = 0.00
0.00 + 2x + x2 = 0 + 24.25
2x + x2 = 0 + 24.25

Combine like terms: 0 + 24.25 = 24.25
2x + x2 = 24.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 24.25 + 1

Reorder the terms:
1 + 2x + x2 = 24.25 + 1

Combine like terms: 24.25 + 1 = 25.25
1 + 2x + x2 = 25.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + 1) equal to 5.024937811 and -5.024937811.

Subproblem 1
x + 1 = 5.024937811

Simplifying
x + 1 = 5.024937811

Reorder the terms:
1 + x = 5.024937811

Solving
1 + x = 5.024937811

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.024937811 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.024937811 + -1
x = 5.024937811 + -1

Combine like terms: 5.024937811 + -1 = 4.024937811
x = 4.024937811

Simplifying
x = 4.024937811

Subproblem 2
x + 1 = -5.024937811

Simplifying
x + 1 = -5.024937811

Reorder the terms:
1 + x = -5.024937811

Solving
1 + x = -5.024937811

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.024937811 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.024937811 + -1
x = -5.024937811 + -1

Combine like terms: -5.024937811 + -1 = -6.024937811
x = -6.024937811

Simplifying
x = -6.024937811

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.024937811, -6.024937811}
Solution
x = {4.024937811, -6.024937811}