SOLUTION: I am supposed to solve this: 3+ root symbol (z-8) = root symbol(z+7) I am not sure what to do here, any help would be appreciated! With explanation if possible!

Question 465887: I am supposed to solve this:
3+ root symbol (z-8) = root symbol(z+7)
I am not sure what to do here, any help would be appreciated! With explanation if possible!
Found 2 solutions by solver91311, bucky:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use sqrt(x) to indicate a radical. Everything inside the parentheses goes inside the radical.

Square both sides, using FOIL in the LHS.

Move all but the remaining radical to the RHS and collect like terms:

Multiply both sides by

Square both sides again:

Substitute this value back into the original equation and do the arithmetic to check the work.

John

My calculator said it, I believe it, that settles it

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
The next step is to square both sides. Squaring the left side is done by multiplying:
.

.
This can be done by using the FOIL method ... multiply First Terms, then Outside Terms, then Inside Terms, and finally Last Terms. When you do that you get:
.

.
This simplifies to:
.
which further simplifies to:
.

.
and the +9 and -8 combines to +1 so the expression reduces to:
.

.
Now return to square the right side of the equation as follows:
.

.
So after squaring both sides the equation becomes:
.

.
Subtract z from both sides reduces this to:
.

.
Next subtract 1 from both sides to get:
.

.
Divide both sides by 6:
.

.
Square both sides:
.

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Finally add 8 to both sides and the result is:
.

.
That's the answer. You can check this by returning to the original equation, substituting 9 for z, and working it out to see that both sides are equal. In other words, start with:
.

.
Substitute 9 for z:
.

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Combine the numbers under each radical to get:
.

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This reduces to:
.

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And this is true (4 does equal 4) so our answer of z = 9 does satisfy the original equation.
.
Hope this helps you to understand that squaring radicals is a way to solve problems such as these.

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