# Solving Complex Equations with x, y, z

• dE_logics
In summary, the conversation is about solving the equation x = ay - (a^2)z for a. The quadratic formula is suggested as a method, but the complexity of the constants x, y, and z is mentioned. It is clarified that the quadratic formula will always work, but it may result in a complex solution. The conversation ends with the quadratic formula being provided and gratitude being expressed for the reminder of its name.
dE_logics
I got this equation -

x = ay - (a^2)z

Solve for a...and apart from the factorization method, is there any other way?...cause the constants x, y, z are very complex formulas.

Last edited:
Are you trying to solve for a or x (the thread title says a, your post says x). If you're solving for x, you just did it... if you're solving for a, just use the quadratic formula. Maybe I'm missing something

Extremely sorry about that...gotta solve for a

Actually x, y, z are very complex (as said) so the quadratic method...I think will not work.

The quadratic formula will always "work". It will just be a very complex solution if x, y, and z are. But no other method is certain to work- and if it did would have to give the same, complex, solution.

humm...ok then, can anyone pls solve it in the quadratic way?...cause we have completely distinct variables...x, y and z.

Then I'll replace the values after the solution.

You have za2 - you + x = 0. So the quadratic formula is:

$$a = \frac{y +/- \sqrt{y^2-4xz}}{2z}$$

Oh yes...I remember...the name of the formula I forgot though...it was somone's name right?...starting with s.

Anyway...thanks man!

Not done maths for a long time.

## 1. How do I solve equations with multiple variables, such as x, y, and z?

To solve equations with multiple variables, you must use a method called substitution. This involves isolating one variable in terms of the others and plugging that value into the other equations to solve for the remaining variables.

## 2. Can I use the same method for solving equations with only two variables?

Yes, the substitution method can also be used for equations with two variables. The key is to isolate one variable and substitute its value into the other equation.

## 3. Are there any other methods for solving complex equations with multiple variables?

Yes, there are other methods such as elimination and graphing. These methods may be more efficient in certain situations, so it is important to learn and understand all of them.

## 4. How do I know if my solution is correct?

To check if your solution is correct, you can substitute the values you obtained for the variables back into the original equations and see if they satisfy the equations. If they do, then your solution is correct.

## 5. Can complex equations with multiple variables have more than one solution?

Yes, it is possible for complex equations with multiple variables to have more than one solution. This can happen when the equations are not independent or when the variables have restrictions on their values.

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