Given: The formula below
[tex]10b=5(\sqrt[]{c}+2[/tex]
To Determine: The equivalent of c given that it was solved to be
[tex]c=(2b-2)^2[/tex]
Solution
[tex]10b=5(\sqrt[]{c}+2)[/tex]
Divide both side by 5 as below
[tex]\begin{gathered} \frac{10b}{5}=\frac{5(\sqrt[]{c}+2)}{5} \\ \frac{10b}{5}=\sqrt[]{c}+2 \end{gathered}[/tex]
Subtract to from both sides
[tex]\begin{gathered} \frac{10b}{5}-2=\sqrt[]{c}+2-2 \\ \frac{10b}{5}-2=\sqrt[]{c} \end{gathered}[/tex]
Make the left hand sides into a single fraction
[tex]\frac{10b-10}{5}=\sqrt[]{c}[/tex]
Take squares of both sides
[tex]\begin{gathered} (\frac{10b-10}{5})^2=(\sqrt[]{c})^2 \\ \frac{(10b-10)^2}{5^2}=c \\ \frac{(10b-10)^2}{25}=c \end{gathered}[/tex]
Hence,
[tex]c=\frac{(10b-10)^2}{25}[/tex]
OPTION D is the correct answer
