7x^2+34x-13=0

Solution for 7x^2+34x-13=0 equation:

Simplifying
7x2 + 34x + -13 = 0

Reorder the terms:
-13 + 34x + 7x2 = 0

Solving
-13 + 34x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-1.857142857 + 4.857142857x + x2 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + 4.857142857x + 1.857142857 + x2 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + 4.857142857x + x2 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + 4.857142857x + x2 = 0 + 1.857142857
4.857142857x + x2 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
4.857142857x + x2 = 1.857142857

The x term is 4.857142857x.  Take half its coefficient (2.428571429).
Square it (5.897959186) and add it to both sides.

Add '5.897959186' to each side of the equation.
4.857142857x + 5.897959186 + x2 = 1.857142857 + 5.897959186

Reorder the terms:
5.897959186 + 4.857142857x + x2 = 1.857142857 + 5.897959186

Combine like terms: 1.857142857 + 5.897959186 = 7.755102043
5.897959186 + 4.857142857x + x2 = 7.755102043

Factor a perfect square on the left side:
(x + 2.428571429)(x + 2.428571429) = 7.755102043

Calculate the square root of the right side: 2.784798385

Break this problem into two subproblems by setting 
(x + 2.428571429) equal to 2.784798385 and -2.784798385.

Subproblem 1
x + 2.428571429 = 2.784798385

Simplifying
x + 2.428571429 = 2.784798385

Reorder the terms:
2.428571429 + x = 2.784798385

Solving
2.428571429 + x = 2.784798385

Solving for variable 'x'.

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

Add '-2.428571429' to each side of the equation.
2.428571429 + -2.428571429 + x = 2.784798385 + -2.428571429

Combine like terms: 2.428571429 + -2.428571429 = 0.000000000
0.000000000 + x = 2.784798385 + -2.428571429
x = 2.784798385 + -2.428571429

Combine like terms: 2.784798385 + -2.428571429 = 0.356226956
x = 0.356226956

Simplifying
x = 0.356226956

Subproblem 2
x + 2.428571429 = -2.784798385

Simplifying
x + 2.428571429 = -2.784798385

Reorder the terms:
2.428571429 + x = -2.784798385

Solving
2.428571429 + x = -2.784798385

Solving for variable 'x'.

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

Add '-2.428571429' to each side of the equation.
2.428571429 + -2.428571429 + x = -2.784798385 + -2.428571429

Combine like terms: 2.428571429 + -2.428571429 = 0.000000000
0.000000000 + x = -2.784798385 + -2.428571429
x = -2.784798385 + -2.428571429

Combine like terms: -2.784798385 + -2.428571429 = -5.213369814
x = -5.213369814

Simplifying
x = -5.213369814

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.356226956, -5.213369814}