0=x^2+7x-6

Solution for 0=x^2+7x-6 equation:

Simplifying
0 = x2 + 7x + -6

Reorder the terms:
0 = -6 + 7x + x2

Solving
0 = -6 + 7x + x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -7x + -1x2 = -6 + 7x + x2 + 6 + -7x + -1x2

Reorder the terms:
6 + -7x + -1x2 = -6 + 6 + 7x + -7x + x2 + -1x2

Combine like terms: -6 + 6 = 0
6 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
6 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
6 + -7x + -1x2 = 0 + x2 + -1x2
6 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 7x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 7x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7x + x2 = 0 + 6
7x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
7x + x2 = 6

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7x + x2 = 18.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
x + 3.5 = 4.272001873

Simplifying
x + 3.5 = 4.272001873

Reorder the terms:
3.5 + x = 4.272001873

Solving
3.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.272001873 + -3.5
x = 4.272001873 + -3.5

Combine like terms: 4.272001873 + -3.5 = 0.772001873
x = 0.772001873

Simplifying
x = 0.772001873

Subproblem 2
x + 3.5 = -4.272001873

Simplifying
x + 3.5 = -4.272001873

Reorder the terms:
3.5 + x = -4.272001873

Solving
3.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.272001873 + -3.5
x = -4.272001873 + -3.5

Combine like terms: -4.272001873 + -3.5 = -7.772001873
x = -7.772001873

Simplifying
x = -7.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.772001873, -7.772001873}