0.5x^2+5x-225=0

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Solution for 0.5x^2+5x-225=0 equation: 


Simplifying
0.5x2 + 5x + -225 = 0

Reorder the terms:
-225 + 5x + 0.5x2 = 0

Solving
-225 + 5x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-450 + 10x + x2 = 0

Move the constant term to the right:

Add '450' to each side of the equation.
-450 + 10x + 450 + x2 = 0 + 450

Reorder the terms:
-450 + 450 + 10x + x2 = 0 + 450

Combine like terms: -450 + 450 = 0
0 + 10x + x2 = 0 + 450
10x + x2 = 0 + 450

Combine like terms: 0 + 450 = 450
10x + x2 = 450

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 450 + 25

Reorder the terms:
25 + 10x + x2 = 450 + 25

Combine like terms: 450 + 25 = 475
25 + 10x + x2 = 475

Factor a perfect square on the left side:
(x + 5)(x + 5) = 475

Calculate the square root of the right side: 21.794494718

Break this problem into two subproblems by setting 
(x + 5) equal to 21.794494718 and -21.794494718.


Subproblem 1
x + 5 = 21.794494718

Simplifying
x + 5 = 21.794494718

Reorder the terms:
5 + x = 21.794494718

Solving
5 + x = 21.794494718

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 21.794494718 + -5

Combine like terms: 5 + -5 = 0
0 + x = 21.794494718 + -5
x = 21.794494718 + -5

Combine like terms: 21.794494718 + -5 = 16.794494718
x = 16.794494718

Simplifying
x = 16.794494718


Subproblem 2
x + 5 = -21.794494718

Simplifying
x + 5 = -21.794494718

Reorder the terms:
5 + x = -21.794494718

Solving
5 + x = -21.794494718

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -21.794494718 + -5

Combine like terms: 5 + -5 = 0
0 + x = -21.794494718 + -5
x = -21.794494718 + -5

Combine like terms: -21.794494718 + -5 = -26.794494718
x = -26.794494718

Simplifying
x = -26.794494718


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.794494718, -26.794494718}

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