Answer
$ k= 4.5,k=2.5$
Work Step by Step
The given expression is
$\Rightarrow 7(2k-7)^2-11=17$
Add $11$ to both sides.
$\Rightarrow 7(2k-7)^2-11+11=17+11$
Simplify.
$\Rightarrow 7(2k-7)^2=28$
Divide both sides by $7$.
$\Rightarrow \frac{7(2k-7)^2}{7}=\frac{28}{7}$
Simplify.
$\Rightarrow (2k-7)^2=4$
Use the square root property.
$\Rightarrow 2k-7=\pm\sqrt{4}$
Simplify.
$\Rightarrow 2k-7=\pm 2$
Separate into two equaitons.
$\Rightarrow 2k-7= 2$ and $2k-7=-2$
Add $7$ to each side of both equations.
$\Rightarrow 2k-7+7= 2+7$ and $2k-7+7=-2+7$
Simplify.
$\Rightarrow 2k= 9$ and $2k=5$
Divide each side of both equations by $2$
$\Rightarrow \frac{2k}{2}= \frac{9}{2}$ and $\frac{2k}{2}=\frac{5}{2}$
Simplify.
$\Rightarrow k= 4.5$ and $k=2.5$
Check both answers using the graph.
The graph is shown below.
