h^2+7h=39

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Solution for h^2+7h=39 equation:


Simplifying
h2 + 7h = 39

Reorder the terms:
7h + h2 = 39

Solving
7h + h2 = 39

Solving for variable 'h'.

Reorder the terms:
-39 + 7h + h2 = 39 + -39

Combine like terms: 39 + -39 = 0
-39 + 7h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 7h + 39 + h2 = 0 + 39

Reorder the terms:
-39 + 39 + 7h + h2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 7h + h2 = 0 + 39
7h + h2 = 0 + 39

Combine like terms: 0 + 39 = 39
7h + h2 = 39

The h term is 7h.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7h + 12.25 + h2 = 39 + 12.25

Reorder the terms:
12.25 + 7h + h2 = 39 + 12.25

Combine like terms: 39 + 12.25 = 51.25
12.25 + 7h + h2 = 51.25

Factor a perfect square on the left side:
(h + 3.5)(h + 3.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(h + 3.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

h + 3.5 = 7.158910532 Simplifying h + 3.5 = 7.158910532 Reorder the terms: 3.5 + h = 7.158910532 Solving 3.5 + h = 7.158910532 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = 7.158910532 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = 7.158910532 + -3.5 h = 7.158910532 + -3.5 Combine like terms: 7.158910532 + -3.5 = 3.658910532 h = 3.658910532 Simplifying h = 3.658910532

Subproblem 2

h + 3.5 = -7.158910532 Simplifying h + 3.5 = -7.158910532 Reorder the terms: 3.5 + h = -7.158910532 Solving 3.5 + h = -7.158910532 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = -7.158910532 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = -7.158910532 + -3.5 h = -7.158910532 + -3.5 Combine like terms: -7.158910532 + -3.5 = -10.658910532 h = -10.658910532 Simplifying h = -10.658910532

Solution

The solution to the problem is based on the solutions from the subproblems. h = {3.658910532, -10.658910532}

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