x^2-9x=43.75

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Solution for x^2-9x=43.75 equation: 


Simplifying
x2 + -9x = 43.75

Reorder the terms:
-9x + x2 = 43.75

Solving
-9x + x2 = 43.75

Solving for variable 'x'.

Reorder the terms:
-43.75 + -9x + x2 = 43.75 + -43.75

Combine like terms: 43.75 + -43.75 = 0.00
-43.75 + -9x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '43.75' to each side of the equation.
-43.75 + -9x + 43.75 + x2 = 0.00 + 43.75

Reorder the terms:
-43.75 + 43.75 + -9x + x2 = 0.00 + 43.75

Combine like terms: -43.75 + 43.75 = 0.00
0.00 + -9x + x2 = 0.00 + 43.75
-9x + x2 = 0.00 + 43.75

Combine like terms: 0.00 + 43.75 = 43.75
-9x + x2 = 43.75

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 43.75 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 43.75 + 20.25

Combine like terms: 43.75 + 20.25 = 64
20.25 + -9x + x2 = 64

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting 
(x + -4.5) equal to 8 and -8.


Subproblem 1
x + -4.5 = 8

Simplifying
x + -4.5 = 8

Reorder the terms:
-4.5 + x = 8

Solving
-4.5 + x = 8

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 8 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 8 + 4.5
x = 8 + 4.5

Combine like terms: 8 + 4.5 = 12.5
x = 12.5

Simplifying
x = 12.5


Subproblem 2
x + -4.5 = -8

Simplifying
x + -4.5 = -8

Reorder the terms:
-4.5 + x = -8

Solving
-4.5 + x = -8

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -8 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -8 + 4.5
x = -8 + 4.5

Combine like terms: -8 + 4.5 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.5, -3.5}

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