h^2+20h=-49

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Solution for h^2+20h=-49 equation:


Simplifying
h2 + 20h = -49

Reorder the terms:
20h + h2 = -49

Solving
20h + h2 = -49

Solving for variable 'h'.

Reorder the terms:
49 + 20h + h2 = -49 + 49

Combine like terms: -49 + 49 = 0
49 + 20h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 20h + -49 + h2 = 0 + -49

Reorder the terms:
49 + -49 + 20h + h2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 20h + h2 = 0 + -49
20h + h2 = 0 + -49

Combine like terms: 0 + -49 = -49
20h + h2 = -49

The h term is 20h.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20h + 100 + h2 = -49 + 100

Reorder the terms:
100 + 20h + h2 = -49 + 100

Combine like terms: -49 + 100 = 51
100 + 20h + h2 = 51

Factor a perfect square on the left side:
(h + 10)(h + 10) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(h + 10) equal to 7.141428429 and -7.141428429.

Subproblem 1

h + 10 = 7.141428429 Simplifying h + 10 = 7.141428429 Reorder the terms: 10 + h = 7.141428429 Solving 10 + h = 7.141428429 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = 7.141428429 + -10 Combine like terms: 10 + -10 = 0 0 + h = 7.141428429 + -10 h = 7.141428429 + -10 Combine like terms: 7.141428429 + -10 = -2.858571571 h = -2.858571571 Simplifying h = -2.858571571

Subproblem 2

h + 10 = -7.141428429 Simplifying h + 10 = -7.141428429 Reorder the terms: 10 + h = -7.141428429 Solving 10 + h = -7.141428429 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = -7.141428429 + -10 Combine like terms: 10 + -10 = 0 0 + h = -7.141428429 + -10 h = -7.141428429 + -10 Combine like terms: -7.141428429 + -10 = -17.141428429 h = -17.141428429 Simplifying h = -17.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. h = {-2.858571571, -17.141428429}

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