114=2x^2+x

Solution for 114=2x^2+x equation:

Simplifying
114 = 2x2 + x

Reorder the terms:
114 = x + 2x2

Solving
114 = x + 2x2

Solving for variable 'x'.

Reorder the terms:
114 + -1x + -2x2 = x + -1x + 2x2 + -2x2

Combine like terms: x + -1x = 0
114 + -1x + -2x2 = 0 + 2x2 + -2x2
114 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
114 + -1x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-57 + 0.5x + x2 = 0

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 0.5x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + 0.5x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 0.5x + x2 = 0 + 57
0.5x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
0.5x + x2 = 57

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 57 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 57 + 0.0625

Combine like terms: 57 + 0.0625 = 57.0625
0.0625 + 0.5x + x2 = 57.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 57.0625

Calculate the square root of the right side: 7.553972465

Break this problem into two subproblems by setting 
(x + 0.25) equal to 7.553972465 and -7.553972465.

Subproblem 1
x + 0.25 = 7.553972465

Simplifying
x + 0.25 = 7.553972465

Reorder the terms:
0.25 + x = 7.553972465

Solving
0.25 + x = 7.553972465

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 7.553972465 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 7.553972465 + -0.25
x = 7.553972465 + -0.25

Combine like terms: 7.553972465 + -0.25 = 7.303972465
x = 7.303972465

Simplifying
x = 7.303972465

Subproblem 2
x + 0.25 = -7.553972465

Simplifying
x + 0.25 = -7.553972465

Reorder the terms:
0.25 + x = -7.553972465

Solving
0.25 + x = -7.553972465

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -7.553972465 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -7.553972465 + -0.25
x = -7.553972465 + -0.25

Combine like terms: -7.553972465 + -0.25 = -7.803972465
x = -7.803972465

Simplifying
x = -7.803972465

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.303972465, -7.803972465}