5x^2-6x-7=0

Solution for 5x^2-6x-7=0 equation:

Simplifying
5x2 + -6x + -7 = 0

Reorder the terms:
-7 + -6x + 5x2 = 0

Solving
-7 + -6x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.4 + -1.2x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -1.2x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -1.2x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -1.2x + x2 = 0 + 1.4
-1.2x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-1.2x + x2 = 1.4

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 1.4 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 1.4 + 0.36

Combine like terms: 1.4 + 0.36 = 1.76
0.36 + -1.2x + x2 = 1.76

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.326649916 and -1.326649916.

Subproblem 1
x + -0.6 = 1.326649916

Simplifying
x + -0.6 = 1.326649916

Reorder the terms:
-0.6 + x = 1.326649916

Solving
-0.6 + x = 1.326649916

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 1.326649916 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 1.326649916 + 0.6
x = 1.326649916 + 0.6

Combine like terms: 1.326649916 + 0.6 = 1.926649916
x = 1.926649916

Simplifying
x = 1.926649916

Subproblem 2
x + -0.6 = -1.326649916

Simplifying
x + -0.6 = -1.326649916

Reorder the terms:
-0.6 + x = -1.326649916

Solving
-0.6 + x = -1.326649916

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -1.326649916 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -1.326649916 + 0.6
x = -1.326649916 + 0.6

Combine like terms: -1.326649916 + 0.6 = -0.726649916
x = -0.726649916

Simplifying
x = -0.726649916

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.926649916, -0.726649916}