7x^2-31x+20=0

Solution for 7x^2-31x+20=0 equation:

Simplifying
7x2 + -31x + 20 = 0

Reorder the terms:
20 + -31x + 7x2 = 0

Solving
20 + -31x + 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'.
2.857142857 + -4.428571429x + x2 = 0

Move the constant term to the right:

Add '-2.857142857' to each side of the equation.
2.857142857 + -4.428571429x + -2.857142857 + x2 = 0 + -2.857142857

Reorder the terms:
2.857142857 + -2.857142857 + -4.428571429x + x2 = 0 + -2.857142857

Combine like terms: 2.857142857 + -2.857142857 = 0.000000000
0.000000000 + -4.428571429x + x2 = 0 + -2.857142857
-4.428571429x + x2 = 0 + -2.857142857

Combine like terms: 0 + -2.857142857 = -2.857142857
-4.428571429x + x2 = -2.857142857

The x term is -4.428571429x.  Take half its coefficient (-2.214285715).
Square it (4.903061228) and add it to both sides.

Add '4.903061228' to each side of the equation.
-4.428571429x + 4.903061228 + x2 = -2.857142857 + 4.903061228

Reorder the terms:
4.903061228 + -4.428571429x + x2 = -2.857142857 + 4.903061228

Combine like terms: -2.857142857 + 4.903061228 = 2.045918371
4.903061228 + -4.428571429x + x2 = 2.045918371

Factor a perfect square on the left side:
(x + -2.214285715)(x + -2.214285715) = 2.045918371

Calculate the square root of the right side: 1.430356029

Break this problem into two subproblems by setting 
(x + -2.214285715) equal to 1.430356029 and -1.430356029.

Subproblem 1
x + -2.214285715 = 1.430356029

Simplifying
x + -2.214285715 = 1.430356029

Reorder the terms:
-2.214285715 + x = 1.430356029

Solving
-2.214285715 + x = 1.430356029

Solving for variable 'x'.

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

Add '2.214285715' to each side of the equation.
-2.214285715 + 2.214285715 + x = 1.430356029 + 2.214285715

Combine like terms: -2.214285715 + 2.214285715 = 0.000000000
0.000000000 + x = 1.430356029 + 2.214285715
x = 1.430356029 + 2.214285715

Combine like terms: 1.430356029 + 2.214285715 = 3.644641744
x = 3.644641744

Simplifying
x = 3.644641744

Subproblem 2
x + -2.214285715 = -1.430356029

Simplifying
x + -2.214285715 = -1.430356029

Reorder the terms:
-2.214285715 + x = -1.430356029

Solving
-2.214285715 + x = -1.430356029

Solving for variable 'x'.

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

Add '2.214285715' to each side of the equation.
-2.214285715 + 2.214285715 + x = -1.430356029 + 2.214285715

Combine like terms: -2.214285715 + 2.214285715 = 0.000000000
0.000000000 + x = -1.430356029 + 2.214285715
x = -1.430356029 + 2.214285715

Combine like terms: -1.430356029 + 2.214285715 = 0.783929686
x = 0.783929686

Simplifying
x = 0.783929686

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.644641744, 0.783929686}