12.25=-0.5x^2+0.5x+15

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Solution for 12.25=-0.5x^2+0.5x+15 equation: 


Simplifying
12.25 = -0.5x2 + 0.5x + 15

Reorder the terms:
12.25 = 15 + 0.5x + -0.5x2

Solving
12.25 = 15 + 0.5x + -0.5x2

Solving for variable 'x'.

Combine like terms: 12.25 + -15 = -2.75
-2.75 + -0.5x + 0.5x2 = 15 + 0.5x + -0.5x2 + -15 + -0.5x + 0.5x2

Reorder the terms:
-2.75 + -0.5x + 0.5x2 = 15 + -15 + 0.5x + -0.5x + -0.5x2 + 0.5x2

Combine like terms: 15 + -15 = 0
-2.75 + -0.5x + 0.5x2 = 0 + 0.5x + -0.5x + -0.5x2 + 0.5x2
-2.75 + -0.5x + 0.5x2 = 0.5x + -0.5x + -0.5x2 + 0.5x2

Combine like terms: 0.5x + -0.5x = 0.0
-2.75 + -0.5x + 0.5x2 = 0.0 + -0.5x2 + 0.5x2
-2.75 + -0.5x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
-2.75 + -0.5x + 0.5x2 = 0.0

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-5.5 + -1x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -1x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -1x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -1x + x2 = 0 + 5.5
-1x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-1x + x2 = 5.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 5.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
0.25 + -1x + x2 = 5.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
x + -0.5 = 2.397915762

Simplifying
x + -0.5 = 2.397915762

Reorder the terms:
-0.5 + x = 2.397915762

Solving
-0.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.397915762 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.397915762 + 0.5
x = 2.397915762 + 0.5

Combine like terms: 2.397915762 + 0.5 = 2.897915762
x = 2.897915762

Simplifying
x = 2.897915762


Subproblem 2
x + -0.5 = -2.397915762

Simplifying
x + -0.5 = -2.397915762

Reorder the terms:
-0.5 + x = -2.397915762

Solving
-0.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.397915762 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.397915762 + 0.5
x = -2.397915762 + 0.5

Combine like terms: -2.397915762 + 0.5 = -1.897915762
x = -1.897915762

Simplifying
x = -1.897915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.897915762, -1.897915762}

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