h^2+9h-18=0

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Solution for h^2+9h-18=0 equation: 


Simplifying
h2 + 9h + -18 = 0

Reorder the terms:
-18 + 9h + h2 = 0

Solving
-18 + 9h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 9h + 18 + h2 = 0 + 18

Reorder the terms:
-18 + 18 + 9h + h2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9h + h2 = 0 + 18
9h + h2 = 0 + 18

Combine like terms: 0 + 18 = 18
9h + h2 = 18

The h term is 9h.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9h + 20.25 + h2 = 18 + 20.25

Reorder the terms:
20.25 + 9h + h2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + 9h + h2 = 38.25

Factor a perfect square on the left side:
(h + 4.5)(h + 4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(h + 4.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
h + 4.5 = 6.184658438

Simplifying
h + 4.5 = 6.184658438

Reorder the terms:
4.5 + h = 6.184658438

Solving
4.5 + h = 6.184658438

Solving for variable 'h'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + h = 6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + h = 6.184658438 + -4.5
h = 6.184658438 + -4.5

Combine like terms: 6.184658438 + -4.5 = 1.684658438
h = 1.684658438

Simplifying
h = 1.684658438


Subproblem 2
h + 4.5 = -6.184658438

Simplifying
h + 4.5 = -6.184658438

Reorder the terms:
4.5 + h = -6.184658438

Solving
4.5 + h = -6.184658438

Solving for variable 'h'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + h = -6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + h = -6.184658438 + -4.5
h = -6.184658438 + -4.5

Combine like terms: -6.184658438 + -4.5 = -10.684658438
h = -10.684658438

Simplifying
h = -10.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.684658438, -10.684658438}

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