h(h+5)=38

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Solution for h(h+5)=38 equation: 


Simplifying
h(h + 5) = 38

Reorder the terms:
h(5 + h) = 38
(5 * h + h * h) = 38
(5h + h2) = 38

Solving
5h + h2 = 38

Solving for variable 'h'.

Reorder the terms:
-38 + 5h + h2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + 5h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 5h + 38 + h2 = 0 + 38

Reorder the terms:
-38 + 38 + 5h + h2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 5h + h2 = 0 + 38
5h + h2 = 0 + 38

Combine like terms: 0 + 38 = 38
5h + h2 = 38

The h term is 5h.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5h + 6.25 + h2 = 38 + 6.25

Reorder the terms:
6.25 + 5h + h2 = 38 + 6.25

Combine like terms: 38 + 6.25 = 44.25
6.25 + 5h + h2 = 44.25

Factor a perfect square on the left side:
(h + 2.5)(h + 2.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(h + 2.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
h + 2.5 = 6.652067348

Simplifying
h + 2.5 = 6.652067348

Reorder the terms:
2.5 + h = 6.652067348

Solving
2.5 + h = 6.652067348

Solving for variable 'h'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + h = 6.652067348 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + h = 6.652067348 + -2.5
h = 6.652067348 + -2.5

Combine like terms: 6.652067348 + -2.5 = 4.152067348
h = 4.152067348

Simplifying
h = 4.152067348


Subproblem 2
h + 2.5 = -6.652067348

Simplifying
h + 2.5 = -6.652067348

Reorder the terms:
2.5 + h = -6.652067348

Solving
2.5 + h = -6.652067348

Solving for variable 'h'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + h = -6.652067348 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + h = -6.652067348 + -2.5
h = -6.652067348 + -2.5

Combine like terms: -6.652067348 + -2.5 = -9.152067348
h = -9.152067348

Simplifying
h = -9.152067348


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {4.152067348, -9.152067348}

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