0=18x-0.22x^2-263

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Solution for 0=18x-0.22x^2-263 equation:


Simplifying
0 = 18x + -0.22x2 + -263

Reorder the terms:
0 = -263 + 18x + -0.22x2

Solving
0 = -263 + 18x + -0.22x2

Solving for variable 'x'.

Combine like terms: 0 + 263 = 263
263 + -18x + 0.22x2 = -263 + 18x + -0.22x2 + 263 + -18x + 0.22x2

Reorder the terms:
263 + -18x + 0.22x2 = -263 + 263 + 18x + -18x + -0.22x2 + 0.22x2

Combine like terms: -263 + 263 = 0
263 + -18x + 0.22x2 = 0 + 18x + -18x + -0.22x2 + 0.22x2
263 + -18x + 0.22x2 = 18x + -18x + -0.22x2 + 0.22x2

Combine like terms: 18x + -18x = 0
263 + -18x + 0.22x2 = 0 + -0.22x2 + 0.22x2
263 + -18x + 0.22x2 = -0.22x2 + 0.22x2

Combine like terms: -0.22x2 + 0.22x2 = 0.00
263 + -18x + 0.22x2 = 0.00

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

Divide each side by '0.22'.
1195.454545 + -81.81818182x + x2 = 0

Move the constant term to the right:

Add '-1195.454545' to each side of the equation.
1195.454545 + -81.81818182x + -1195.454545 + x2 = 0 + -1195.454545

Reorder the terms:
1195.454545 + -1195.454545 + -81.81818182x + x2 = 0 + -1195.454545

Combine like terms: 1195.454545 + -1195.454545 = 0.000000
0.000000 + -81.81818182x + x2 = 0 + -1195.454545
-81.81818182x + x2 = 0 + -1195.454545

Combine like terms: 0 + -1195.454545 = -1195.454545
-81.81818182x + x2 = -1195.454545

The x term is -81.81818182x.  Take half its coefficient (-40.90909091).
Square it (1673.553719) and add it to both sides.

Add '1673.553719' to each side of the equation.
-81.81818182x + 1673.553719 + x2 = -1195.454545 + 1673.553719

Reorder the terms:
1673.553719 + -81.81818182x + x2 = -1195.454545 + 1673.553719

Combine like terms: -1195.454545 + 1673.553719 = 478.099174
1673.553719 + -81.81818182x + x2 = 478.099174

Factor a perfect square on the left side:
(x + -40.90909091)(x + -40.90909091) = 478.099174

Calculate the square root of the right side: 21.865479048

Break this problem into two subproblems by setting 
(x + -40.90909091) equal to 21.865479048 and -21.865479048.

Subproblem 1

x + -40.90909091 = 21.865479048 Simplifying x + -40.90909091 = 21.865479048 Reorder the terms: -40.90909091 + x = 21.865479048 Solving -40.90909091 + x = 21.865479048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.90909091' to each side of the equation. -40.90909091 + 40.90909091 + x = 21.865479048 + 40.90909091 Combine like terms: -40.90909091 + 40.90909091 = 0.00000000 0.00000000 + x = 21.865479048 + 40.90909091 x = 21.865479048 + 40.90909091 Combine like terms: 21.865479048 + 40.90909091 = 62.774569958 x = 62.774569958 Simplifying x = 62.774569958

Subproblem 2

x + -40.90909091 = -21.865479048 Simplifying x + -40.90909091 = -21.865479048 Reorder the terms: -40.90909091 + x = -21.865479048 Solving -40.90909091 + x = -21.865479048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.90909091' to each side of the equation. -40.90909091 + 40.90909091 + x = -21.865479048 + 40.90909091 Combine like terms: -40.90909091 + 40.90909091 = 0.00000000 0.00000000 + x = -21.865479048 + 40.90909091 x = -21.865479048 + 40.90909091 Combine like terms: -21.865479048 + 40.90909091 = 19.043611862 x = 19.043611862 Simplifying x = 19.043611862

Solution

The solution to the problem is based on the solutions from the subproblems. x = {62.774569958, 19.043611862}

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