4x^2+8x-34=0

Solution for 4x^2+8x-34=0 equation:

Simplifying
4x2 + 8x + -34 = 0

Reorder the terms:
-34 + 8x + 4x2 = 0

Solving
-34 + 8x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 4x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
-17 + 4x + 2x2 = 0

Solving
-17 + 4x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + 2x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 2x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 2x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 2x + x2 = 0 + 8.5
2x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
2x + x2 = 8.5

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 = 8.5 + 1

Reorder the terms:
1 + 2x + x2 = 8.5 + 1

Combine like terms: 8.5 + 1 = 9.5
1 + 2x + x2 = 9.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9.5

Calculate the square root of the right side: 3.082207001

Break this problem into two subproblems by setting 
(x + 1) equal to 3.082207001 and -3.082207001.

Subproblem 1
x + 1 = 3.082207001

Simplifying
x + 1 = 3.082207001

Reorder the terms:
1 + x = 3.082207001

Solving
1 + x = 3.082207001

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 = 3.082207001 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.082207001 + -1
x = 3.082207001 + -1

Combine like terms: 3.082207001 + -1 = 2.082207001
x = 2.082207001

Simplifying
x = 2.082207001

Subproblem 2
x + 1 = -3.082207001

Simplifying
x + 1 = -3.082207001

Reorder the terms:
1 + x = -3.082207001

Solving
1 + x = -3.082207001

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 = -3.082207001 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.082207001 + -1
x = -3.082207001 + -1

Combine like terms: -3.082207001 + -1 = -4.082207001
x = -4.082207001

Simplifying
x = -4.082207001

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.082207001, -4.082207001}
Solution
x = {2.082207001, -4.082207001}