Question

Help Please!!

x-8 = -sqrt symbol(x^2 - 8)

If you notice, there is a negative sign in front of the square root symbol, or radical. if I have to eliminate the symbol (I would square the terms under the sign) would I distribute the negative sign? Or only give it to the first term? Or is there something else I am supposed to do?

Help is greatly appreciated!

Answer 1

`\bf x-8=-√(x^2-8)\implies x-8=-1√(x^2-8)\implies \cfrac{x-8}{-1}=√(x^2-8) \\\\\\ 8-x=√(x^2-8)\impliedby \textit{now, squaring both sides} \\\\\\ (8-x)^2=x^2-8\implies (8-x)(8-x)=x^2-8\impliedby FOIL \\\\\\ 64-16x+x^2=x^2-8\implies 64+8-16x+x^2-x^2=0 \\\\\\ 72-16x=0\implies \cfrac{72}{16}=x\implies \cfrac{9}{2}=x`