7x^2-19x-8=

Solution for 7x^2-19x-8= equation:

Simplifying
7x2 + -19x + -8 = 0

Reorder the terms:
-8 + -19x + 7x2 = 0

Solving
-8 + -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'.
-1.142857143 + -2.714285714x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -2.714285714x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -2.714285714x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -2.714285714x + x2 = 0 + 1.142857143
-2.714285714x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-2.714285714x + x2 = 1.142857143

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 = 1.142857143 + 1.841836734

Reorder the terms:
1.841836734 + -2.714285714x + x2 = 1.142857143 + 1.841836734

Combine like terms: 1.142857143 + 1.841836734 = 2.984693877
1.841836734 + -2.714285714x + x2 = 2.984693877

Factor a perfect square on the left side:
(x + -1.357142857)(x + -1.357142857) = 2.984693877

Calculate the square root of the right side: 1.72762666

Break this problem into two subproblems by setting 
(x + -1.357142857) equal to 1.72762666 and -1.72762666.

Subproblem 1
x + -1.357142857 = 1.72762666

Simplifying
x + -1.357142857 = 1.72762666

Reorder the terms:
-1.357142857 + x = 1.72762666

Solving
-1.357142857 + x = 1.72762666

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 = 1.72762666 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + x = 1.72762666 + 1.357142857
x = 1.72762666 + 1.357142857

Combine like terms: 1.72762666 + 1.357142857 = 3.084769517
x = 3.084769517

Simplifying
x = 3.084769517

Subproblem 2
x + -1.357142857 = -1.72762666

Simplifying
x + -1.357142857 = -1.72762666

Reorder the terms:
-1.357142857 + x = -1.72762666

Solving
-1.357142857 + x = -1.72762666

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 = -1.72762666 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + x = -1.72762666 + 1.357142857
x = -1.72762666 + 1.357142857

Combine like terms: -1.72762666 + 1.357142857 = -0.370483803
x = -0.370483803

Simplifying
x = -0.370483803

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.084769517, -0.370483803}