x^2-3x=22.167

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Solution for x^2-3x=22.167 equation: 


Simplifying
x2 + -3x = 22.167

Reorder the terms:
-3x + x2 = 22.167

Solving
-3x + x2 = 22.167

Solving for variable 'x'.

Reorder the terms:
-22.167 + -3x + x2 = 22.167 + -22.167

Combine like terms: 22.167 + -22.167 = 0.000
-22.167 + -3x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '22.167' to each side of the equation.
-22.167 + -3x + 22.167 + x2 = 0.000 + 22.167

Reorder the terms:
-22.167 + 22.167 + -3x + x2 = 0.000 + 22.167

Combine like terms: -22.167 + 22.167 = 0.000
0.000 + -3x + x2 = 0.000 + 22.167
-3x + x2 = 0.000 + 22.167

Combine like terms: 0.000 + 22.167 = 22.167
-3x + x2 = 22.167

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 22.167 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 22.167 + 2.25

Combine like terms: 22.167 + 2.25 = 24.417
2.25 + -3x + x2 = 24.417

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 24.417

Calculate the square root of the right side: 4.941356089

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.941356089 and -4.941356089.


Subproblem 1
x + -1.5 = 4.941356089

Simplifying
x + -1.5 = 4.941356089

Reorder the terms:
-1.5 + x = 4.941356089

Solving
-1.5 + x = 4.941356089

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.941356089 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.941356089 + 1.5
x = 4.941356089 + 1.5

Combine like terms: 4.941356089 + 1.5 = 6.441356089
x = 6.441356089

Simplifying
x = 6.441356089


Subproblem 2
x + -1.5 = -4.941356089

Simplifying
x + -1.5 = -4.941356089

Reorder the terms:
-1.5 + x = -4.941356089

Solving
-1.5 + x = -4.941356089

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.941356089 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.941356089 + 1.5
x = -4.941356089 + 1.5

Combine like terms: -4.941356089 + 1.5 = -3.441356089
x = -3.441356089

Simplifying
x = -3.441356089


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.441356089, -3.441356089}

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