3h^2-72h+93=0

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Solution for 3h^2-72h+93=0 equation: 


Simplifying
3h2 + -72h + 93 = 0

Reorder the terms:
93 + -72h + 3h2 = 0

Solving
93 + -72h + 3h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(31 + -24h + h2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(31 + -24h + h2)' equal to zero and attempt to solve:

Simplifying
31 + -24h + h2 = 0

Solving
31 + -24h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -24h + -31 + h2 = 0 + -31

Reorder the terms:
31 + -31 + -24h + h2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -24h + h2 = 0 + -31
-24h + h2 = 0 + -31

Combine like terms: 0 + -31 = -31
-24h + h2 = -31

The h term is -24h.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24h + 144 + h2 = -31 + 144

Reorder the terms:
144 + -24h + h2 = -31 + 144

Combine like terms: -31 + 144 = 113
144 + -24h + h2 = 113

Factor a perfect square on the left side:
(h + -12)(h + -12) = 113

Calculate the square root of the right side: 10.630145813

Break this problem into two subproblems by setting 
(h + -12) equal to 10.630145813 and -10.630145813.


Subproblem 1
h + -12 = 10.630145813

Simplifying
h + -12 = 10.630145813

Reorder the terms:
-12 + h = 10.630145813

Solving
-12 + h = 10.630145813

Solving for variable 'h'.

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

Add '12' to each side of the equation.
-12 + 12 + h = 10.630145813 + 12

Combine like terms: -12 + 12 = 0
0 + h = 10.630145813 + 12
h = 10.630145813 + 12

Combine like terms: 10.630145813 + 12 = 22.630145813
h = 22.630145813

Simplifying
h = 22.630145813


Subproblem 2
h + -12 = -10.630145813

Simplifying
h + -12 = -10.630145813

Reorder the terms:
-12 + h = -10.630145813

Solving
-12 + h = -10.630145813

Solving for variable 'h'.

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

Add '12' to each side of the equation.
-12 + 12 + h = -10.630145813 + 12

Combine like terms: -12 + 12 = 0
0 + h = -10.630145813 + 12
h = -10.630145813 + 12

Combine like terms: -10.630145813 + 12 = 1.369854187
h = 1.369854187

Simplifying
h = 1.369854187


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {22.630145813, 1.369854187}
Solution
h = {22.630145813, 1.369854187}

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