476=x^2+31x+238

Solution for 476=x^2+31x+238 equation:

Simplifying
476 = x2 + 31x + 238

Reorder the terms:
476 = 238 + 31x + x2

Solving
476 = 238 + 31x + x2

Solving for variable 'x'.

Combine like terms: 476 + -238 = 238
238 + -31x + -1x2 = 238 + 31x + x2 + -238 + -31x + -1x2

Reorder the terms:
238 + -31x + -1x2 = 238 + -238 + 31x + -31x + x2 + -1x2

Combine like terms: 238 + -238 = 0
238 + -31x + -1x2 = 0 + 31x + -31x + x2 + -1x2
238 + -31x + -1x2 = 31x + -31x + x2 + -1x2

Combine like terms: 31x + -31x = 0
238 + -31x + -1x2 = 0 + x2 + -1x2
238 + -31x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
238 + -31x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-238 + 31x + x2 = 0

Move the constant term to the right:

Add '238' to each side of the equation.
-238 + 31x + 238 + x2 = 0 + 238

Reorder the terms:
-238 + 238 + 31x + x2 = 0 + 238

Combine like terms: -238 + 238 = 0
0 + 31x + x2 = 0 + 238
31x + x2 = 0 + 238

Combine like terms: 0 + 238 = 238
31x + x2 = 238

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = 238 + 240.25

Reorder the terms:
240.25 + 31x + x2 = 238 + 240.25

Combine like terms: 238 + 240.25 = 478.25
240.25 + 31x + x2 = 478.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 478.25

Calculate the square root of the right side: 21.868927729

Break this problem into two subproblems by setting 
(x + 15.5) equal to 21.868927729 and -21.868927729.

Subproblem 1
x + 15.5 = 21.868927729

Simplifying
x + 15.5 = 21.868927729

Reorder the terms:
15.5 + x = 21.868927729

Solving
15.5 + x = 21.868927729

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = 21.868927729 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = 21.868927729 + -15.5
x = 21.868927729 + -15.5

Combine like terms: 21.868927729 + -15.5 = 6.368927729
x = 6.368927729

Simplifying
x = 6.368927729

Subproblem 2
x + 15.5 = -21.868927729

Simplifying
x + 15.5 = -21.868927729

Reorder the terms:
15.5 + x = -21.868927729

Solving
15.5 + x = -21.868927729

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = -21.868927729 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = -21.868927729 + -15.5
x = -21.868927729 + -15.5

Combine like terms: -21.868927729 + -15.5 = -37.368927729
x = -37.368927729

Simplifying
x = -37.368927729

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.368927729, -37.368927729}