h^2+25h+36=0

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Solution for h^2+25h+36=0 equation: 


Simplifying
h2 + 25h + 36 = 0

Reorder the terms:
36 + 25h + h2 = 0

Solving
36 + 25h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 25h + -36 + h2 = 0 + -36

Reorder the terms:
36 + -36 + 25h + h2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 25h + h2 = 0 + -36
25h + h2 = 0 + -36

Combine like terms: 0 + -36 = -36
25h + h2 = -36

The h term is 25h.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25h + 156.25 + h2 = -36 + 156.25

Reorder the terms:
156.25 + 25h + h2 = -36 + 156.25

Combine like terms: -36 + 156.25 = 120.25
156.25 + 25h + h2 = 120.25

Factor a perfect square on the left side:
(h + 12.5)(h + 12.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(h + 12.5) equal to 10.9658561 and -10.9658561.


Subproblem 1
h + 12.5 = 10.9658561

Simplifying
h + 12.5 = 10.9658561

Reorder the terms:
12.5 + h = 10.9658561

Solving
12.5 + h = 10.9658561

Solving for variable 'h'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + h = 10.9658561 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + h = 10.9658561 + -12.5
h = 10.9658561 + -12.5

Combine like terms: 10.9658561 + -12.5 = -1.5341439
h = -1.5341439

Simplifying
h = -1.5341439


Subproblem 2
h + 12.5 = -10.9658561

Simplifying
h + 12.5 = -10.9658561

Reorder the terms:
12.5 + h = -10.9658561

Solving
12.5 + h = -10.9658561

Solving for variable 'h'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + h = -10.9658561 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + h = -10.9658561 + -12.5
h = -10.9658561 + -12.5

Combine like terms: -10.9658561 + -12.5 = -23.4658561
h = -23.4658561

Simplifying
h = -23.4658561


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {-1.5341439, -23.4658561}

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