x^2-0.5x-9=0

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Solution for x^2-0.5x-9=0 equation: 


Simplifying
x2 + -0.5x + -9 = 0

Reorder the terms:
-9 + -0.5x + x2 = 0

Solving
-9 + -0.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -0.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -0.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -0.5x + x2 = 0 + 9
-0.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-0.5x + x2 = 9

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 9 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 9 + 0.0625

Combine like terms: 9 + 0.0625 = 9.0625
0.0625 + -0.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -0.25) equal to 3.010398645 and -3.010398645.


Subproblem 1
x + -0.25 = 3.010398645

Simplifying
x + -0.25 = 3.010398645

Reorder the terms:
-0.25 + x = 3.010398645

Solving
-0.25 + x = 3.010398645

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 3.010398645 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 3.010398645 + 0.25
x = 3.010398645 + 0.25

Combine like terms: 3.010398645 + 0.25 = 3.260398645
x = 3.260398645

Simplifying
x = 3.260398645


Subproblem 2
x + -0.25 = -3.010398645

Simplifying
x + -0.25 = -3.010398645

Reorder the terms:
-0.25 + x = -3.010398645

Solving
-0.25 + x = -3.010398645

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -3.010398645 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -3.010398645 + 0.25
x = -3.010398645 + 0.25

Combine like terms: -3.010398645 + 0.25 = -2.760398645
x = -2.760398645

Simplifying
x = -2.760398645


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.260398645, -2.760398645}

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