Question

Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 7t+5−−−−−√=7 Enter the exact answers.

Answer 1

The given equation is

`\sqrt[]{7t+5}=7`

Square both sides to cancel the square root

`\begin{gathered} (\sqrt[]{7t+5})^2=(7)^2 \\ 7t+5=49 \end{gathered}`

Subtract 5 from both sides

`\begin{gathered} 7t+5-5=49-5 \\ 7t=44 \end{gathered}`

Divide both sides by 7

`\begin{gathered} (7t)/(7)=(44)/(7) \\ t=(44)/(7) \\ t=6(2)/(7) \end{gathered}`

The solution is t = 44/7 OR t = 6 2/7 (mixed number)