h^2-10h-4=0

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Solution for h^2-10h-4=0 equation: 


Simplifying
h2 + -10h + -4 = 0

Reorder the terms:
-4 + -10h + h2 = 0

Solving
-4 + -10h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -10h + 4 + h2 = 0 + 4

Reorder the terms:
-4 + 4 + -10h + h2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -10h + h2 = 0 + 4
-10h + h2 = 0 + 4

Combine like terms: 0 + 4 = 4
-10h + h2 = 4

The h term is -10h.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10h + 25 + h2 = 4 + 25

Reorder the terms:
25 + -10h + h2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + -10h + h2 = 29

Factor a perfect square on the left side:
(h + -5)(h + -5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(h + -5) equal to 5.385164807 and -5.385164807.


Subproblem 1
h + -5 = 5.385164807

Simplifying
h + -5 = 5.385164807

Reorder the terms:
-5 + h = 5.385164807

Solving
-5 + h = 5.385164807

Solving for variable 'h'.

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

Add '5' to each side of the equation.
-5 + 5 + h = 5.385164807 + 5

Combine like terms: -5 + 5 = 0
0 + h = 5.385164807 + 5
h = 5.385164807 + 5

Combine like terms: 5.385164807 + 5 = 10.385164807
h = 10.385164807

Simplifying
h = 10.385164807


Subproblem 2
h + -5 = -5.385164807

Simplifying
h + -5 = -5.385164807

Reorder the terms:
-5 + h = -5.385164807

Solving
-5 + h = -5.385164807

Solving for variable 'h'.

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

Add '5' to each side of the equation.
-5 + 5 + h = -5.385164807 + 5

Combine like terms: -5 + 5 = 0
0 + h = -5.385164807 + 5
h = -5.385164807 + 5

Combine like terms: -5.385164807 + 5 = -0.385164807
h = -0.385164807

Simplifying
h = -0.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {10.385164807, -0.385164807}

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