x^2-3x=7.5

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Solution for x^2-3x=7.5 equation: 


Simplifying
x2 + -3x = 7.5

Reorder the terms:
-3x + x2 = 7.5

Solving
-3x + x2 = 7.5

Solving for variable 'x'.

Reorder the terms:
-7.5 + -3x + x2 = 7.5 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
-7.5 + -3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -3x + 7.5 + x2 = 0.0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -3x + x2 = 0.0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -3x + x2 = 0.0 + 7.5
-3x + x2 = 0.0 + 7.5

Combine like terms: 0.0 + 7.5 = 7.5
-3x + x2 = 7.5

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 = 7.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + -3x + x2 = 9.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + -1.5 = 3.122498999

Simplifying
x + -1.5 = 3.122498999

Reorder the terms:
-1.5 + x = 3.122498999

Solving
-1.5 + x = 3.122498999

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 = 3.122498999 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.122498999 + 1.5
x = 3.122498999 + 1.5

Combine like terms: 3.122498999 + 1.5 = 4.622498999
x = 4.622498999

Simplifying
x = 4.622498999


Subproblem 2
x + -1.5 = -3.122498999

Simplifying
x + -1.5 = -3.122498999

Reorder the terms:
-1.5 + x = -3.122498999

Solving
-1.5 + x = -3.122498999

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 = -3.122498999 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.122498999 + 1.5
x = -3.122498999 + 1.5

Combine like terms: -3.122498999 + 1.5 = -1.622498999
x = -1.622498999

Simplifying
x = -1.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.622498999, -1.622498999}

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