Having some trouble with this problem. I feel like I'm doing it incorrectly. Can someone show me how to do this step by step?
for
Hello, DasRabbit!
Since you're having trouble with this problem,
. . I thought some baby-steps might be in order.
We have:$\displaystyle \text{Solve for }x\!:\;\;-3\sqrt{x+4} + 10 \:=\:7$
. . $\displaystyle \text{-}3\sqrt{x+4} + 10 \:=\:7$
Subtract 10 from both sides:
. . $\displaystyle \text{-}3\sqrt{x+4} + 10 \:{\color{red}-\: 10} \:=\:7 \:{\color{red}-\: 10}\quad\Rightarrow\quad \text{-}3\sqrt{x+4} \:=\:\text{-}3$
Divide both sides by -3:
. . $\displaystyle \frac{\text{-}3\sqrt{x+4}}{{\color{red}\text{-}3}} \:=\:\frac{\text{-}3}{{\color{red}\text{-}3}} \quad\Rightarrow\quad \sqrt{x+4} \:=\:1$
Square both sides:
. . $\displaystyle (\sqrt{x+4})^{\color{red}2} \:=\: (1)^{\color{red}2} \quad\Rightarrow\quad x + 4 \:=\:1$
Subtract 4 from both sides:
. . $\displaystyle x + 4 \:{\color{red}-\: 4} \:=\:1 \:{\color{red}-\: 4} \quad\Rightarrow\quad \boxed{x \:=\:\text{-}3}$