7x^2-19x-7=0

Solution for 7x^2-19x-7=0 equation:

Simplifying
7x2 + -19x + -7 = 0

Reorder the terms:
-7 + -19x + 7x2 = 0

Solving
-7 + -19x + 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 + -2.714285714x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.714285714x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.714285714x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.714285714x + x2 = 0 + 1
-2.714285714x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.714285714x + x2 = 1

The x term is -2.714285714x.  Take half its coefficient (-1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
-2.714285714x + 1.841836734 + x2 = 1 + 1.841836734

Reorder the terms:
1.841836734 + -2.714285714x + x2 = 1 + 1.841836734

Combine like terms: 1 + 1.841836734 = 2.841836734
1.841836734 + -2.714285714x + x2 = 2.841836734

Factor a perfect square on the left side:
(x + -1.357142857)(x + -1.357142857) = 2.841836734

Calculate the square root of the right side: 1.685774817

Break this problem into two subproblems by setting 
(x + -1.357142857) equal to 1.685774817 and -1.685774817.

Subproblem 1
x + -1.357142857 = 1.685774817

Simplifying
x + -1.357142857 = 1.685774817

Reorder the terms:
-1.357142857 + x = 1.685774817

Solving
-1.357142857 + x = 1.685774817

Solving for variable 'x'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + x = 1.685774817 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + x = 1.685774817 + 1.357142857
x = 1.685774817 + 1.357142857

Combine like terms: 1.685774817 + 1.357142857 = 3.042917674
x = 3.042917674

Simplifying
x = 3.042917674

Subproblem 2
x + -1.357142857 = -1.685774817

Simplifying
x + -1.357142857 = -1.685774817

Reorder the terms:
-1.357142857 + x = -1.685774817

Solving
-1.357142857 + x = -1.685774817

Solving for variable 'x'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + x = -1.685774817 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + x = -1.685774817 + 1.357142857
x = -1.685774817 + 1.357142857

Combine like terms: -1.685774817 + 1.357142857 = -0.32863196
x = -0.32863196

Simplifying
x = -0.32863196

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.042917674, -0.32863196}