7x^2+x=5

Solution for 7x^2+x=5 equation:

Simplifying
7x2 + x = 5

Reorder the terms:
x + 7x2 = 5

Solving
x + 7x2 = 5

Solving for variable 'x'.

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

Combine like terms: 5 + -5 = 0
-5 + x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 0.1428571429x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 0.1428571429x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 0.1428571429x + x2 = 0 + 0.7142857143
0.1428571429x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
0.1428571429x + x2 = 0.7142857143

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1428571429x + 0.25 + x2 = 0.7142857143 + 0.25

Reorder the terms:
0.25 + 0.1428571429x + x2 = 0.7142857143 + 0.25

Combine like terms: 0.7142857143 + 0.25 = 0.9642857143
0.25 + 0.1428571429x + x2 = 0.9642857143

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.9642857143

Calculate the square root of the right side: 0.981980506

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.981980506 and -0.981980506.

Subproblem 1
x + 0.5 = 0.981980506

Simplifying
x + 0.5 = 0.981980506

Reorder the terms:
0.5 + x = 0.981980506

Solving
0.5 + x = 0.981980506

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.981980506 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.981980506 + -0.5
x = 0.981980506 + -0.5

Combine like terms: 0.981980506 + -0.5 = 0.481980506
x = 0.481980506

Simplifying
x = 0.481980506

Subproblem 2
x + 0.5 = -0.981980506

Simplifying
x + 0.5 = -0.981980506

Reorder the terms:
0.5 + x = -0.981980506

Solving
0.5 + x = -0.981980506

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.981980506 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.981980506 + -0.5
x = -0.981980506 + -0.5

Combine like terms: -0.981980506 + -0.5 = -1.481980506
x = -1.481980506

Simplifying
x = -1.481980506

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.481980506, -1.481980506}