Question

Solve $9m^2-12m+4=25$.

Short answer

The solutions are$m=-1,m=\frac{7}{3}$.

Step-by-step solution

Given Information.      

The Given equation is $9m^2-12m+4=25$.

Factor the trinomial. 

$$\begin{gathered} (3m{)}^2-3·4·m+4=25 \\ (3m-2{)}^2=25 \end{gathered}$$

Use square root property.

$$\begin{gathered} 3m-2=\pm \sqrt{25} \\ 3m-2=\pm 5 \end{gathered}$$

Isolate the term.    

$$\begin{gathered} 3m=2\pm 5 \\ m=\frac{2\pm 5}{3} \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} m=\frac{2+5}{3}=\frac{7}{3} \\ m=\frac{2-5}{3}=\frac{-3}{3}=-1 \end{gathered}$$

The solutions are$m=-1,m=\frac{7}{3}$.