Question 465887
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Use sqrt(x) to indicate a radical.  Everything inside the parentheses goes inside the radical.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\ +\ \sqrt{z\ -\ 8}\ =\ \sqrt{z\ +\ 7}]


Square both sides, using FOIL in the LHS.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9\ +\ 6\sqrt{z\ -\ 8}\ +\ (z\ -\ 8)\ =\ z\ +\ 7]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -6\sqrt{z\ -\ 8}\ =\ -6]


Multiply both sides by *[tex \Large -\frac{1}{6}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{z\ -\ 8}\ =\ 1]


Square both sides again:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z\ -\ 8\ =\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z\ =\ 9]


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


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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