SOLUTION: how is the following equation solved z - 7z1/2 + 12 = 0

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Question 261529: how is the following equation solved
z - 7z1/2 + 12 = 0

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

The key to solving this equation is to recognize that . This is what makes this a quadratic equation. If you have trouble seeing this, then we can use a temporary variable:
Let
then
Replacing z and with and q respectively your equation becomes:

This is clearly a quadratic equation. We can solve this by factoring:

From the Zero Product Property we know that this product can be zero only if one of the factors is zero. So:
or
Solving these we get:
or

Of course we are not interested in what q is. We want a solution for z. So at this point we replace q with :
or
We now have one more step. We need to square both sides of these equations giving us:
or

Using a temporary variable is not required. But they can be helpful until you get used to working without them. Here is a solution which does not use a temporary variable:

Factor:

Zero Product Property:
or
Solve:
or
or

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