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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
(