This is my second question – Blue Rocket Academy

Learn Pythagoras Theorem

Sure, here’s how to solve for k:

$\sqrt{2k^2 + 5} = 8$

To isolate k, we can square both sides of the equation:

$(\sqrt{2k^2 + 5})^2 = 8^2$

Simplifying the left-hand side:

$2k^2 + 5 = 64$

Subtracting 5 from both sides:

$2k^2 = 59$

Dividing both sides by 2:

$k^2 = \frac{59}{2}$

Taking the square root of both sides:

$k = \pm \sqrt{\frac{59}{2}}$

So the solutions for k are:

$k = \sqrt{\frac{59}{2}} \approx 4.07$

$k = -\sqrt{\frac{59}{2}} \approx -4.07$

Note that we took the positive and negative square root because the original equation was an equation of a square root.