4h^2-56h-172=0

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Solution for 4h^2-56h-172=0 equation: 


Simplifying
4h2 + -56h + -172 = 0

Reorder the terms:
-172 + -56h + 4h2 = 0

Solving
-172 + -56h + 4h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-43 + -14h + h2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-43 + -14h + h2)' equal to zero and attempt to solve:

Simplifying
-43 + -14h + h2 = 0

Solving
-43 + -14h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -14h + 43 + h2 = 0 + 43

Reorder the terms:
-43 + 43 + -14h + h2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -14h + h2 = 0 + 43
-14h + h2 = 0 + 43

Combine like terms: 0 + 43 = 43
-14h + h2 = 43

The h term is -14h.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14h + 49 + h2 = 43 + 49

Reorder the terms:
49 + -14h + h2 = 43 + 49

Combine like terms: 43 + 49 = 92
49 + -14h + h2 = 92

Factor a perfect square on the left side:
(h + -7)(h + -7) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(h + -7) equal to 9.591663047 and -9.591663047.


Subproblem 1
h + -7 = 9.591663047

Simplifying
h + -7 = 9.591663047

Reorder the terms:
-7 + h = 9.591663047

Solving
-7 + h = 9.591663047

Solving for variable 'h'.

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

Add '7' to each side of the equation.
-7 + 7 + h = 9.591663047 + 7

Combine like terms: -7 + 7 = 0
0 + h = 9.591663047 + 7
h = 9.591663047 + 7

Combine like terms: 9.591663047 + 7 = 16.591663047
h = 16.591663047

Simplifying
h = 16.591663047


Subproblem 2
h + -7 = -9.591663047

Simplifying
h + -7 = -9.591663047

Reorder the terms:
-7 + h = -9.591663047

Solving
-7 + h = -9.591663047

Solving for variable 'h'.

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

Add '7' to each side of the equation.
-7 + 7 + h = -9.591663047 + 7

Combine like terms: -7 + 7 = 0
0 + h = -9.591663047 + 7
h = -9.591663047 + 7

Combine like terms: -9.591663047 + 7 = -2.591663047
h = -2.591663047

Simplifying
h = -2.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {16.591663047, -2.591663047}
Solution
h = {16.591663047, -2.591663047}

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