Given: The formula below
![10b=5(\sqrt[]{c}+2](https://img.qammunity.org/2023/formulas/mathematics/college/d1crpq5ioz71fqcz7gtfzd314qy0sqzs8j.png)
To Determine: The equivalent of c given that it was solved to be

Solution
![10b=5(\sqrt[]{c}+2)](https://img.qammunity.org/2023/formulas/mathematics/college/gmieh740y6swgxjjzk47b3tspcm61i2u3q.png)
Divide both side by 5 as below
![\begin{gathered} (10b)/(5)=\frac{5(\sqrt[]{c}+2)}{5} \\ (10b)/(5)=\sqrt[]{c}+2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/aomjugzw7awg5doou0halt2dxtgwl770hx.png)
Subtract to from both sides
![\begin{gathered} (10b)/(5)-2=\sqrt[]{c}+2-2 \\ (10b)/(5)-2=\sqrt[]{c} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/jex5sts84wowwxt50g92bv2pzl6dix8bhp.png)
Make the left hand sides into a single fraction
![(10b-10)/(5)=\sqrt[]{c}](https://img.qammunity.org/2023/formulas/mathematics/college/cc947y0d5jhftqsafn85yql62tiph41cx3.png)
Take squares of both sides
![\begin{gathered} ((10b-10)/(5))^2=(\sqrt[]{c})^2 \\ ((10b-10)^2)/(5^2)=c \\ ((10b-10)^2)/(25)=c \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/cpbjjfm5xeo6mclsl69e3mt08pfk66a100.png)
Hence,

OPTION D is the correct answer