# Criteria for Solving this equation

• smooney
In summary, the conversation discusses the possibility of solving a fifth order polynomial equation without knowing any numerical values. It is mentioned that there is no general formula for solving this type of equation, but an iterative procedure using Excel can be used if numerical values are available. It is also noted that there is a more complex formula involving special functions, but it is easier to use numerical methods in practice.
smooney
Is it possible to solve this equation in terms of H without knowing any numbers? If so what method would I use? If I had numbers I think I could solve it numerically in excel. It's been a few years since I was in school and am fairly (very) rusty:

H^5 -10*L*H^4 +25*L^2*H^3 -25*Q^2/K^2 = 0

L,K = Constant

Any help would be appreciated, Thanks!

You have a fifth order polynomial in H. There is no general formula which can solve this equation. If you have numerical values for your constants, then an iterative procedure (perhaps using Excel) would be the way to calculate solutions.

There is no simple formula giving Y as a function of L, H, Q, K because it is a polynomial equation of the fifth degree.
Such formula exists, but involving special functions : the Jacobi theta functions. But, in practice, it is much simpler to use numerical methods to solve the equation.

## 1. What is the purpose of criteria in solving an equation?

The purpose of criteria in solving an equation is to provide a set of guidelines or rules that can be used to determine the correct solution to the equation. These criteria help to narrow down the possible solutions and ensure that the final answer is accurate and reliable.

## 2. How do you determine the criteria for solving a particular equation?

The criteria for solving an equation are determined by the properties and rules of the mathematical operations involved. These can include properties of addition, subtraction, multiplication, division, exponents, and logarithms. Additionally, any given equation may have specific criteria based on its unique structure.

## 3. Can criteria for solving an equation vary depending on the type of equation?

Yes, the criteria for solving an equation can vary depending on the type of equation. For example, the criteria for solving a linear equation will be different from that of a quadratic equation. It is important to understand the specific criteria for each type of equation in order to solve them correctly.

## 4. What happens if the criteria for solving an equation are not followed?

If the criteria for solving an equation are not followed, the solution may not be accurate or may not exist at all. This can lead to incorrect results and a misunderstanding of the problem. It is important to carefully follow the criteria in order to obtain the correct solution.

## 5. Can criteria for solving an equation change over time?

No, the criteria for solving an equation do not change over time. These criteria are based on the fundamental rules and properties of mathematics and are universally applicable. However, new equations may be discovered that require different criteria for solving them, but the existing criteria will still remain valid for other equations.

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