9h^2+3h-19=

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Solution for 9h^2+3h-19= equation: 


Simplifying
9h2 + 3h + -19 = 0

Reorder the terms:
-19 + 3h + 9h2 = 0

Solving
-19 + 3h + 9h2 = 0

Solving for variable 'h'.

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

Divide each side by '9'.
-2.111111111 + 0.3333333333h + h2 = 0

Move the constant term to the right:

Add '2.111111111' to each side of the equation.
-2.111111111 + 0.3333333333h + 2.111111111 + h2 = 0 + 2.111111111

Reorder the terms:
-2.111111111 + 2.111111111 + 0.3333333333h + h2 = 0 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + 0.3333333333h + h2 = 0 + 2.111111111
0.3333333333h + h2 = 0 + 2.111111111

Combine like terms: 0 + 2.111111111 = 2.111111111
0.3333333333h + h2 = 2.111111111

The h term is 0.3333333333h.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333h + 0.02777777779 + h2 = 2.111111111 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333h + h2 = 2.111111111 + 0.02777777779

Combine like terms: 2.111111111 + 0.02777777779 = 2.13888888879
0.02777777779 + 0.3333333333h + h2 = 2.13888888879

Factor a perfect square on the left side:
(h + 0.1666666667)(h + 0.1666666667) = 2.13888888879

Calculate the square root of the right side: 1.462494065

Break this problem into two subproblems by setting 
(h + 0.1666666667) equal to 1.462494065 and -1.462494065.


Subproblem 1
h + 0.1666666667 = 1.462494065

Simplifying
h + 0.1666666667 = 1.462494065

Reorder the terms:
0.1666666667 + h = 1.462494065

Solving
0.1666666667 + h = 1.462494065

Solving for variable 'h'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + h = 1.462494065 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + h = 1.462494065 + -0.1666666667
h = 1.462494065 + -0.1666666667

Combine like terms: 1.462494065 + -0.1666666667 = 1.2958273983
h = 1.2958273983

Simplifying
h = 1.2958273983


Subproblem 2
h + 0.1666666667 = -1.462494065

Simplifying
h + 0.1666666667 = -1.462494065

Reorder the terms:
0.1666666667 + h = -1.462494065

Solving
0.1666666667 + h = -1.462494065

Solving for variable 'h'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + h = -1.462494065 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + h = -1.462494065 + -0.1666666667
h = -1.462494065 + -0.1666666667

Combine like terms: -1.462494065 + -0.1666666667 = -1.6291607317
h = -1.6291607317

Simplifying
h = -1.6291607317


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.2958273983, -1.6291607317}

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