h^2+16h-20=0

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Solution for h^2+16h-20=0 equation: 


Simplifying
h2 + 16h + -20 = 0

Reorder the terms:
-20 + 16h + h2 = 0

Solving
-20 + 16h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 16h + 20 + h2 = 0 + 20

Reorder the terms:
-20 + 20 + 16h + h2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 16h + h2 = 0 + 20
16h + h2 = 0 + 20

Combine like terms: 0 + 20 = 20
16h + h2 = 20

The h term is 16h.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16h + 64 + h2 = 20 + 64

Reorder the terms:
64 + 16h + h2 = 20 + 64

Combine like terms: 20 + 64 = 84
64 + 16h + h2 = 84

Factor a perfect square on the left side:
(h + 8)(h + 8) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(h + 8) equal to 9.16515139 and -9.16515139.


Subproblem 1
h + 8 = 9.16515139

Simplifying
h + 8 = 9.16515139

Reorder the terms:
8 + h = 9.16515139

Solving
8 + h = 9.16515139

Solving for variable 'h'.

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

Add '-8' to each side of the equation.
8 + -8 + h = 9.16515139 + -8

Combine like terms: 8 + -8 = 0
0 + h = 9.16515139 + -8
h = 9.16515139 + -8

Combine like terms: 9.16515139 + -8 = 1.16515139
h = 1.16515139

Simplifying
h = 1.16515139


Subproblem 2
h + 8 = -9.16515139

Simplifying
h + 8 = -9.16515139

Reorder the terms:
8 + h = -9.16515139

Solving
8 + h = -9.16515139

Solving for variable 'h'.

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

Add '-8' to each side of the equation.
8 + -8 + h = -9.16515139 + -8

Combine like terms: 8 + -8 = 0
0 + h = -9.16515139 + -8
h = -9.16515139 + -8

Combine like terms: -9.16515139 + -8 = -17.16515139
h = -17.16515139

Simplifying
h = -17.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.16515139, -17.16515139}

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