x^2+18.5x-36=0

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Solution for x^2+18.5x-36=0 equation: 


Simplifying
x2 + 18.5x + -36 = 0

Reorder the terms:
-36 + 18.5x + x2 = 0

Solving
-36 + 18.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 18.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 18.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 18.5x + x2 = 0 + 36
18.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
18.5x + x2 = 36

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 = 36 + 85.5625

Reorder the terms:
85.5625 + 18.5x + x2 = 36 + 85.5625

Combine like terms: 36 + 85.5625 = 121.5625
85.5625 + 18.5x + x2 = 121.5625

Factor a perfect square on the left side:
(x + 9.25)(x + 9.25) = 121.5625

Calculate the square root of the right side: 11.025538536

Break this problem into two subproblems by setting 
(x + 9.25) equal to 11.025538536 and -11.025538536.


Subproblem 1
x + 9.25 = 11.025538536

Simplifying
x + 9.25 = 11.025538536

Reorder the terms:
9.25 + x = 11.025538536

Solving
9.25 + x = 11.025538536

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 = 11.025538536 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = 11.025538536 + -9.25
x = 11.025538536 + -9.25

Combine like terms: 11.025538536 + -9.25 = 1.775538536
x = 1.775538536

Simplifying
x = 1.775538536


Subproblem 2
x + 9.25 = -11.025538536

Simplifying
x + 9.25 = -11.025538536

Reorder the terms:
9.25 + x = -11.025538536

Solving
9.25 + x = -11.025538536

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 = -11.025538536 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = -11.025538536 + -9.25
x = -11.025538536 + -9.25

Combine like terms: -11.025538536 + -9.25 = -20.275538536
x = -20.275538536

Simplifying
x = -20.275538536


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.775538536, -20.275538536}

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