x^2-3x=2.25

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Solution for x^2-3x=2.25 equation:


Simplifying
x2 + -3x = 2.25

Reorder the terms:
-3x + x2 = 2.25

Solving
-3x + x2 = 2.25

Solving for variable 'x'.

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

Combine like terms: 2.25 + -2.25 = 0.00
-2.25 + -3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -3x + 2.25 + x2 = 0.00 + 2.25

Reorder the terms:
-2.25 + 2.25 + -3x + x2 = 0.00 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -3x + x2 = 0.00 + 2.25
-3x + x2 = 0.00 + 2.25

Combine like terms: 0.00 + 2.25 = 2.25
-3x + x2 = 2.25

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 = 2.25 + 2.25

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

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + -3x + x2 = 4.5

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.121320344 and -2.121320344.


Subproblem 1
x + -1.5 = 2.121320344

Simplifying
x + -1.5 = 2.121320344

Reorder the terms:
-1.5 + x = 2.121320344

Solving
-1.5 + x = 2.121320344

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 = 2.121320344 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.121320344 + 1.5
x = 2.121320344 + 1.5

Combine like terms: 2.121320344 + 1.5 = 3.621320344
x = 3.621320344

Simplifying
x = 3.621320344


Subproblem 2
x + -1.5 = -2.121320344

Simplifying
x + -1.5 = -2.121320344

Reorder the terms:
-1.5 + x = -2.121320344

Solving
-1.5 + x = -2.121320344

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 = -2.121320344 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.121320344 + 1.5
x = -2.121320344 + 1.5

Combine like terms: -2.121320344 + 1.5 = -0.621320344
x = -0.621320344

Simplifying
x = -0.621320344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.621320344, -0.621320344}

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