x^2+18.5x-225=0

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Solution for x^2+18.5x-225=0 equation: 


Simplifying
x2 + 18.5x + -225 = 0

Reorder the terms:
-225 + 18.5x + x2 = 0

Solving
-225 + 18.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 18.5x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + 18.5x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 18.5x + x2 = 0 + 225
18.5x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
18.5x + x2 = 225

The x term is 18.5x.  Take half its coefficient (9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
18.5x + 85.5625 + x2 = 225 + 85.5625

Reorder the terms:
85.5625 + 18.5x + x2 = 225 + 85.5625

Combine like terms: 225 + 85.5625 = 310.5625
85.5625 + 18.5x + x2 = 310.5625

Factor a perfect square on the left side:
(x + 9.25)(x + 9.25) = 310.5625

Calculate the square root of the right side: 17.622783549

Break this problem into two subproblems by setting 
(x + 9.25) equal to 17.622783549 and -17.622783549.


Subproblem 1
x + 9.25 = 17.622783549

Simplifying
x + 9.25 = 17.622783549

Reorder the terms:
9.25 + x = 17.622783549

Solving
9.25 + x = 17.622783549

Solving for variable 'x'.

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

Add '-9.25' to each side of the equation.
9.25 + -9.25 + x = 17.622783549 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = 17.622783549 + -9.25
x = 17.622783549 + -9.25

Combine like terms: 17.622783549 + -9.25 = 8.372783549
x = 8.372783549

Simplifying
x = 8.372783549


Subproblem 2
x + 9.25 = -17.622783549

Simplifying
x + 9.25 = -17.622783549

Reorder the terms:
9.25 + x = -17.622783549

Solving
9.25 + x = -17.622783549

Solving for variable 'x'.

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

Add '-9.25' to each side of the equation.
9.25 + -9.25 + x = -17.622783549 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = -17.622783549 + -9.25
x = -17.622783549 + -9.25

Combine like terms: -17.622783549 + -9.25 = -26.872783549
x = -26.872783549

Simplifying
x = -26.872783549


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.372783549, -26.872783549}

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