x^2-4x-18.09=0

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Solution for x^2-4x-18.09=0 equation: 


Simplifying
x2 + -4x + -18.09 = 0

Reorder the terms:
-18.09 + -4x + x2 = 0

Solving
-18.09 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18.09' to each side of the equation.
-18.09 + -4x + 18.09 + x2 = 0 + 18.09

Reorder the terms:
-18.09 + 18.09 + -4x + x2 = 0 + 18.09

Combine like terms: -18.09 + 18.09 = 0.00
0.00 + -4x + x2 = 0 + 18.09
-4x + x2 = 0 + 18.09

Combine like terms: 0 + 18.09 = 18.09
-4x + x2 = 18.09

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 18.09 + 4

Reorder the terms:
4 + -4x + x2 = 18.09 + 4

Combine like terms: 18.09 + 4 = 22.09
4 + -4x + x2 = 22.09

Factor a perfect square on the left side:
(x + -2)(x + -2) = 22.09

Calculate the square root of the right side: 4.7

Break this problem into two subproblems by setting 
(x + -2) equal to 4.7 and -4.7.


Subproblem 1
x + -2 = 4.7

Simplifying
x + -2 = 4.7

Reorder the terms:
-2 + x = 4.7

Solving
-2 + x = 4.7

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.7 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.7 + 2
x = 4.7 + 2

Combine like terms: 4.7 + 2 = 6.7
x = 6.7

Simplifying
x = 6.7


Subproblem 2
x + -2 = -4.7

Simplifying
x + -2 = -4.7

Reorder the terms:
-2 + x = -4.7

Solving
-2 + x = -4.7

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.7 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.7 + 2
x = -4.7 + 2

Combine like terms: -4.7 + 2 = -2.7
x = -2.7

Simplifying
x = -2.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.7, -2.7}

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