9.14*12=2x+2x^2

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Solution for 9.14*12=2x+2x^2 equation: 


Simplifying
9.14 * 12 = 2x + 2x2

Multiply 9.14 * 12
109.68 = 2x + 2x2

Solving
109.68 = 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
109.68 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
109.68 + -2x + -2x2 = 0 + 2x2 + -2x2
109.68 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
109.68 + -2x + -2x2 = 0

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

Divide each side by '-2'.
-54.84 + x + x2 = 0

Move the constant term to the right:

Add '54.84' to each side of the equation.
-54.84 + x + 54.84 + x2 = 0 + 54.84

Reorder the terms:
-54.84 + 54.84 + x + x2 = 0 + 54.84

Combine like terms: -54.84 + 54.84 = 0.00
0.00 + x + x2 = 0 + 54.84
x + x2 = 0 + 54.84

Combine like terms: 0 + 54.84 = 54.84
x + x2 = 54.84

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.
 + 0.25 + x2 = 54.84 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 54.84 + 0.25

Combine like terms: 54.84 + 0.25 = 55.09
1.25 + x2 = 55.09

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 55.09

Calculate the square root of the right side: 7.422263806

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.422263806 and -7.422263806.


Subproblem 1
x + 0.5 = 7.422263806

Simplifying
x + 0.5 = 7.422263806

Reorder the terms:
0.5 + x = 7.422263806

Solving
0.5 + x = 7.422263806

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 = 7.422263806 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 7.422263806 + -0.5
x = 7.422263806 + -0.5

Combine like terms: 7.422263806 + -0.5 = 6.922263806
x = 6.922263806

Simplifying
x = 6.922263806


Subproblem 2
x + 0.5 = -7.422263806

Simplifying
x + 0.5 = -7.422263806

Reorder the terms:
0.5 + x = -7.422263806

Solving
0.5 + x = -7.422263806

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 = -7.422263806 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -7.422263806 + -0.5
x = -7.422263806 + -0.5

Combine like terms: -7.422263806 + -0.5 = -7.922263806
x = -7.922263806

Simplifying
x = -7.922263806


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.922263806, -7.922263806}

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