7x^2+x=150

Solution for 7x^2+x=150 equation:

Simplifying
7x2 + x = 150

Reorder the terms:
x + 7x2 = 150

Solving
x + 7x2 = 150

Solving for variable 'x'.

Reorder the terms:
-150 + x + 7x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + x + 7x2 = 0

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

Divide each side by '7'.
-21.42857143 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '21.42857143' to each side of the equation.
-21.42857143 + 0.1428571429x + 21.42857143 + x2 = 0 + 21.42857143

Reorder the terms:
-21.42857143 + 21.42857143 + 0.1428571429x + x2 = 0 + 21.42857143

Combine like terms: -21.42857143 + 21.42857143 = 0.00000000
0.00000000 + 0.1428571429x + x2 = 0 + 21.42857143
0.1428571429x + x2 = 0 + 21.42857143

Combine like terms: 0 + 21.42857143 = 21.42857143
0.1428571429x + x2 = 21.42857143

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 = 21.42857143 + 0.25

Reorder the terms:
0.25 + 0.1428571429x + x2 = 21.42857143 + 0.25

Combine like terms: 21.42857143 + 0.25 = 21.67857143
0.25 + 0.1428571429x + x2 = 21.67857143

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 21.67857143

Calculate the square root of the right side: 4.656025282

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.656025282 and -4.656025282.

Subproblem 1
x + 0.5 = 4.656025282

Simplifying
x + 0.5 = 4.656025282

Reorder the terms:
0.5 + x = 4.656025282

Solving
0.5 + x = 4.656025282

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 = 4.656025282 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.656025282 + -0.5
x = 4.656025282 + -0.5

Combine like terms: 4.656025282 + -0.5 = 4.156025282
x = 4.156025282

Simplifying
x = 4.156025282

Subproblem 2
x + 0.5 = -4.656025282

Simplifying
x + 0.5 = -4.656025282

Reorder the terms:
0.5 + x = -4.656025282

Solving
0.5 + x = -4.656025282

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 = -4.656025282 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.656025282 + -0.5
x = -4.656025282 + -0.5

Combine like terms: -4.656025282 + -0.5 = -5.156025282
x = -5.156025282

Simplifying
x = -5.156025282

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.156025282, -5.156025282}