h*h+29h-28=0

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Solution for h*h+29h-28=0 equation: 


Simplifying
h * h + 29h + -28 = 0

Multiply h * h
h2 + 29h + -28 = 0

Reorder the terms:
-28 + 29h + h2 = 0

Solving
-28 + 29h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 29h + 28 + h2 = 0 + 28

Reorder the terms:
-28 + 28 + 29h + h2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 29h + h2 = 0 + 28
29h + h2 = 0 + 28

Combine like terms: 0 + 28 = 28
29h + h2 = 28

The h term is 29h.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29h + 210.25 + h2 = 28 + 210.25

Reorder the terms:
210.25 + 29h + h2 = 28 + 210.25

Combine like terms: 28 + 210.25 = 238.25
210.25 + 29h + h2 = 238.25

Factor a perfect square on the left side:
(h + 14.5)(h + 14.5) = 238.25

Calculate the square root of the right side: 15.43534904

Break this problem into two subproblems by setting 
(h + 14.5) equal to 15.43534904 and -15.43534904.


Subproblem 1
h + 14.5 = 15.43534904

Simplifying
h + 14.5 = 15.43534904

Reorder the terms:
14.5 + h = 15.43534904

Solving
14.5 + h = 15.43534904

Solving for variable 'h'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + h = 15.43534904 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + h = 15.43534904 + -14.5
h = 15.43534904 + -14.5

Combine like terms: 15.43534904 + -14.5 = 0.93534904
h = 0.93534904

Simplifying
h = 0.93534904


Subproblem 2
h + 14.5 = -15.43534904

Simplifying
h + 14.5 = -15.43534904

Reorder the terms:
14.5 + h = -15.43534904

Solving
14.5 + h = -15.43534904

Solving for variable 'h'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + h = -15.43534904 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + h = -15.43534904 + -14.5
h = -15.43534904 + -14.5

Combine like terms: -15.43534904 + -14.5 = -29.93534904
h = -29.93534904

Simplifying
h = -29.93534904


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.93534904, -29.93534904}

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