x^2-3x=1.8

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Solution for x^2-3x=1.8 equation: 


Simplifying
x2 + -3x = 1.8

Reorder the terms:
-3x + x2 = 1.8

Solving
-3x + x2 = 1.8

Solving for variable 'x'.

Reorder the terms:
-1.8 + -3x + x2 = 1.8 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
-1.8 + -3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -3x + 1.8 + x2 = 0.0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -3x + x2 = 0.0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -3x + x2 = 0.0 + 1.8
-3x + x2 = 0.0 + 1.8

Combine like terms: 0.0 + 1.8 = 1.8
-3x + x2 = 1.8

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 = 1.8 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1.8 + 2.25

Combine like terms: 1.8 + 2.25 = 4.05
2.25 + -3x + x2 = 4.05

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.05

Calculate the square root of the right side: 2.01246118

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.01246118 and -2.01246118.


Subproblem 1
x + -1.5 = 2.01246118

Simplifying
x + -1.5 = 2.01246118

Reorder the terms:
-1.5 + x = 2.01246118

Solving
-1.5 + x = 2.01246118

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 = 2.01246118 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.01246118 + 1.5
x = 2.01246118 + 1.5

Combine like terms: 2.01246118 + 1.5 = 3.51246118
x = 3.51246118

Simplifying
x = 3.51246118


Subproblem 2
x + -1.5 = -2.01246118

Simplifying
x + -1.5 = -2.01246118

Reorder the terms:
-1.5 + x = -2.01246118

Solving
-1.5 + x = -2.01246118

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 = -2.01246118 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.01246118 + 1.5
x = -2.01246118 + 1.5

Combine like terms: -2.01246118 + 1.5 = -0.51246118
x = -0.51246118

Simplifying
x = -0.51246118


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.51246118, -0.51246118}

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