11.4=.218x^2-2.54x+18.5

Solution for 11.4=.218x^2-2.54x+18.5 equation:

Simplifying
11.4 = 0.218x2 + -2.54x + 18.5

Reorder the terms:
11.4 = 18.5 + -2.54x + 0.218x2

Solving
11.4 = 18.5 + -2.54x + 0.218x2

Solving for variable 'x'.

Combine like terms: 11.4 + -18.5 = -7.1
-7.1 + 2.54x + -0.218x2 = 18.5 + -2.54x + 0.218x2 + -18.5 + 2.54x + -0.218x2

Reorder the terms:
-7.1 + 2.54x + -0.218x2 = 18.5 + -18.5 + -2.54x + 2.54x + 0.218x2 + -0.218x2

Combine like terms: 18.5 + -18.5 = 0.0
-7.1 + 2.54x + -0.218x2 = 0.0 + -2.54x + 2.54x + 0.218x2 + -0.218x2
-7.1 + 2.54x + -0.218x2 = -2.54x + 2.54x + 0.218x2 + -0.218x2

Combine like terms: -2.54x + 2.54x = 0.00
-7.1 + 2.54x + -0.218x2 = 0.00 + 0.218x2 + -0.218x2
-7.1 + 2.54x + -0.218x2 = 0.218x2 + -0.218x2

Combine like terms: 0.218x2 + -0.218x2 = 0.000
-7.1 + 2.54x + -0.218x2 = 0.000

Begin completing the square.  Divide all terms by
-0.218 the coefficient of the squared term: 

Divide each side by '-0.218'.
32.56880734 + -11.65137615x + x2 = 0

Move the constant term to the right:

Add '-32.56880734' to each side of the equation.
32.56880734 + -11.65137615x + -32.56880734 + x2 = 0 + -32.56880734

Reorder the terms:
32.56880734 + -32.56880734 + -11.65137615x + x2 = 0 + -32.56880734

Combine like terms: 32.56880734 + -32.56880734 = 0.00000000
0.00000000 + -11.65137615x + x2 = 0 + -32.56880734
-11.65137615x + x2 = 0 + -32.56880734

Combine like terms: 0 + -32.56880734 = -32.56880734
-11.65137615x + x2 = -32.56880734

The x term is -11.65137615x.  Take half its coefficient (-5.825688075).
Square it (33.93864155) and add it to both sides.

Add '33.93864155' to each side of the equation.
-11.65137615x + 33.93864155 + x2 = -32.56880734 + 33.93864155

Reorder the terms:
33.93864155 + -11.65137615x + x2 = -32.56880734 + 33.93864155

Combine like terms: -32.56880734 + 33.93864155 = 1.36983421
33.93864155 + -11.65137615x + x2 = 1.36983421

Factor a perfect square on the left side:
(x + -5.825688075)(x + -5.825688075) = 1.36983421

Calculate the square root of the right side: 1.170399167

Break this problem into two subproblems by setting 
(x + -5.825688075) equal to 1.170399167 and -1.170399167.

Subproblem 1
x + -5.825688075 = 1.170399167

Simplifying
x + -5.825688075 = 1.170399167

Reorder the terms:
-5.825688075 + x = 1.170399167

Solving
-5.825688075 + x = 1.170399167

Solving for variable 'x'.

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

Add '5.825688075' to each side of the equation.
-5.825688075 + 5.825688075 + x = 1.170399167 + 5.825688075

Combine like terms: -5.825688075 + 5.825688075 = 0.000000000
0.000000000 + x = 1.170399167 + 5.825688075
x = 1.170399167 + 5.825688075

Combine like terms: 1.170399167 + 5.825688075 = 6.996087242
x = 6.996087242

Simplifying
x = 6.996087242

Subproblem 2
x + -5.825688075 = -1.170399167

Simplifying
x + -5.825688075 = -1.170399167

Reorder the terms:
-5.825688075 + x = -1.170399167

Solving
-5.825688075 + x = -1.170399167

Solving for variable 'x'.

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

Add '5.825688075' to each side of the equation.
-5.825688075 + 5.825688075 + x = -1.170399167 + 5.825688075

Combine like terms: -5.825688075 + 5.825688075 = 0.000000000
0.000000000 + x = -1.170399167 + 5.825688075
x = -1.170399167 + 5.825688075

Combine like terms: -1.170399167 + 5.825688075 = 4.655288908
x = 4.655288908

Simplifying
x = 4.655288908

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.996087242, 4.655288908}