7x^2-22x-3=0

Solution for 7x^2-22x-3=0 equation:

Simplifying
7x2 + -22x + -3 = 0

Reorder the terms:
-3 + -22x + 7x2 = 0

Solving
-3 + -22x + 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'.
-0.4285714286 + -3.142857143x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -3.142857143x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -3.142857143x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -3.142857143x + x2 = 0 + 0.4285714286
-3.142857143x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-3.142857143x + x2 = 0.4285714286

The x term is -3.142857143x.  Take half its coefficient (-1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
-3.142857143x + 2.469387757 + x2 = 0.4285714286 + 2.469387757

Reorder the terms:
2.469387757 + -3.142857143x + x2 = 0.4285714286 + 2.469387757

Combine like terms: 0.4285714286 + 2.469387757 = 2.8979591856
2.469387757 + -3.142857143x + x2 = 2.8979591856

Factor a perfect square on the left side:
(x + -1.571428572)(x + -1.571428572) = 2.8979591856

Calculate the square root of the right side: 1.702339327

Break this problem into two subproblems by setting 
(x + -1.571428572) equal to 1.702339327 and -1.702339327.

Subproblem 1
x + -1.571428572 = 1.702339327

Simplifying
x + -1.571428572 = 1.702339327

Reorder the terms:
-1.571428572 + x = 1.702339327

Solving
-1.571428572 + x = 1.702339327

Solving for variable 'x'.

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

Add '1.571428572' to each side of the equation.
-1.571428572 + 1.571428572 + x = 1.702339327 + 1.571428572

Combine like terms: -1.571428572 + 1.571428572 = 0.000000000
0.000000000 + x = 1.702339327 + 1.571428572
x = 1.702339327 + 1.571428572

Combine like terms: 1.702339327 + 1.571428572 = 3.273767899
x = 3.273767899

Simplifying
x = 3.273767899

Subproblem 2
x + -1.571428572 = -1.702339327

Simplifying
x + -1.571428572 = -1.702339327

Reorder the terms:
-1.571428572 + x = -1.702339327

Solving
-1.571428572 + x = -1.702339327

Solving for variable 'x'.

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

Add '1.571428572' to each side of the equation.
-1.571428572 + 1.571428572 + x = -1.702339327 + 1.571428572

Combine like terms: -1.571428572 + 1.571428572 = 0.000000000
0.000000000 + x = -1.702339327 + 1.571428572
x = -1.702339327 + 1.571428572

Combine like terms: -1.702339327 + 1.571428572 = -0.130910755
x = -0.130910755

Simplifying
x = -0.130910755

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.273767899, -0.130910755}