x^2-3x=46.75

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Solution for x^2-3x=46.75 equation: 


Simplifying
x2 + -3x = 46.75

Reorder the terms:
-3x + x2 = 46.75

Solving
-3x + x2 = 46.75

Solving for variable 'x'.

Reorder the terms:
-46.75 + -3x + x2 = 46.75 + -46.75

Combine like terms: 46.75 + -46.75 = 0.00
-46.75 + -3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '46.75' to each side of the equation.
-46.75 + -3x + 46.75 + x2 = 0.00 + 46.75

Reorder the terms:
-46.75 + 46.75 + -3x + x2 = 0.00 + 46.75

Combine like terms: -46.75 + 46.75 = 0.00
0.00 + -3x + x2 = 0.00 + 46.75
-3x + x2 = 0.00 + 46.75

Combine like terms: 0.00 + 46.75 = 46.75
-3x + x2 = 46.75

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 = 46.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 46.75 + 2.25

Combine like terms: 46.75 + 2.25 = 49
2.25 + -3x + x2 = 49

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + -1.5) equal to 7 and -7.


Subproblem 1
x + -1.5 = 7

Simplifying
x + -1.5 = 7

Reorder the terms:
-1.5 + x = 7

Solving
-1.5 + x = 7

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 = 7 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 7 + 1.5
x = 7 + 1.5

Combine like terms: 7 + 1.5 = 8.5
x = 8.5

Simplifying
x = 8.5


Subproblem 2
x + -1.5 = -7

Simplifying
x + -1.5 = -7

Reorder the terms:
-1.5 + x = -7

Solving
-1.5 + x = -7

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 = -7 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -7 + 1.5
x = -7 + 1.5

Combine like terms: -7 + 1.5 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.5, -5.5}

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