x^2-9x-20.25=42.25

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Solution for x^2-9x-20.25=42.25 equation: 


Simplifying
x2 + -9x + -20.25 = 42.25

Reorder the terms:
-20.25 + -9x + x2 = 42.25

Solving
-20.25 + -9x + x2 = 42.25

Solving for variable 'x'.

Reorder the terms:
-20.25 + -42.25 + -9x + x2 = 42.25 + -42.25

Combine like terms: -20.25 + -42.25 = -62.5
-62.5 + -9x + x2 = 42.25 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
-62.5 + -9x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + -9x + 62.5 + x2 = 0.00 + 62.5

Reorder the terms:
-62.5 + 62.5 + -9x + x2 = 0.00 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + -9x + x2 = 0.00 + 62.5
-9x + x2 = 0.00 + 62.5

Combine like terms: 0.00 + 62.5 = 62.5
-9x + x2 = 62.5

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 = 62.5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 62.5 + 20.25

Combine like terms: 62.5 + 20.25 = 82.75
20.25 + -9x + x2 = 82.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 82.75

Calculate the square root of the right side: 9.096702699

Break this problem into two subproblems by setting 
(x + -4.5) equal to 9.096702699 and -9.096702699.


Subproblem 1
x + -4.5 = 9.096702699

Simplifying
x + -4.5 = 9.096702699

Reorder the terms:
-4.5 + x = 9.096702699

Solving
-4.5 + x = 9.096702699

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 = 9.096702699 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 9.096702699 + 4.5
x = 9.096702699 + 4.5

Combine like terms: 9.096702699 + 4.5 = 13.596702699
x = 13.596702699

Simplifying
x = 13.596702699


Subproblem 2
x + -4.5 = -9.096702699

Simplifying
x + -4.5 = -9.096702699

Reorder the terms:
-4.5 + x = -9.096702699

Solving
-4.5 + x = -9.096702699

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 = -9.096702699 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -9.096702699 + 4.5
x = -9.096702699 + 4.5

Combine like terms: -9.096702699 + 4.5 = -4.596702699
x = -4.596702699

Simplifying
x = -4.596702699


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.596702699, -4.596702699}

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