h*h+10h=21

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Solution for h*h+10h=21 equation:


Simplifying
h * h + 10h = 21

Multiply h * h
h2 + 10h = 21

Reorder the terms:
10h + h2 = 21

Solving
10h + h2 = 21

Solving for variable 'h'.

Reorder the terms:
-21 + 10h + h2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 10h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 10h + 21 + h2 = 0 + 21

Reorder the terms:
-21 + 21 + 10h + h2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 10h + h2 = 0 + 21
10h + h2 = 0 + 21

Combine like terms: 0 + 21 = 21
10h + h2 = 21

The h term is 10h.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10h + 25 + h2 = 21 + 25

Reorder the terms:
25 + 10h + h2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + 10h + h2 = 46

Factor a perfect square on the left side:
(h + 5)(h + 5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(h + 5) equal to 6.782329983 and -6.782329983.

Subproblem 1

h + 5 = 6.782329983 Simplifying h + 5 = 6.782329983 Reorder the terms: 5 + h = 6.782329983 Solving 5 + h = 6.782329983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = 6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + h = 6.782329983 + -5 h = 6.782329983 + -5 Combine like terms: 6.782329983 + -5 = 1.782329983 h = 1.782329983 Simplifying h = 1.782329983

Subproblem 2

h + 5 = -6.782329983 Simplifying h + 5 = -6.782329983 Reorder the terms: 5 + h = -6.782329983 Solving 5 + h = -6.782329983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = -6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + h = -6.782329983 + -5 h = -6.782329983 + -5 Combine like terms: -6.782329983 + -5 = -11.782329983 h = -11.782329983 Simplifying h = -11.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1.782329983, -11.782329983}

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