# If #8sqrt(4z^2 - 43) = 40#, what is the value of #z#?

##### 2 Answers

Assumption: the question is:

#### Explanation:

This is done in stages. First you have all the terms with z on the LHS of = and all the terms without z on the other side.

Then you manipulate the LHS side until the only thing left is the single z.

Add 43 to both sides giving

Divide both sides by 8. Same as multiply by

But

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

But

Write as:

Taking the root

divide both side by 2 to get rid of the 2 from

After testing

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check: Consider the left hand side only for

But

Thus LHS=RHS so

#### Explanation:

Isolate the square-root.

Checking in the original equation, both solutions work.