Question

Solve$\frac{1}{2}{x}^2+4=24$

Short answer

The solutions are$x=2\sqrt{10},x=-2\sqrt{10}$.

Step-by-step solution

Given Information.  

The Given equation is $\frac{1}{2}{x}^2+4=24$.

Isolate the quadratic term and makes its coefficient one.   

$$\begin{gathered} \frac{1}{2}{x}^2+4=24 \\ \frac{1}{2}{x}^2=24-4 \\ \frac{1}{2}{x}^2=20 \end{gathered}$$

Divide both sides by $\frac{1}{2}$.

$$\begin{gathered} x^2=20\times 2 \\ {x}^2=40 \end{gathered}$$

 Use the square root property.  

$x=\pm \sqrt{40}$

Simplify the radical by factoring the radicand.

$x=\pm \sqrt{2\times 2\times 2\times 5}$

$x=\pm 2\sqrt{10}$

Rewrite to show two solutions.

$x=2\sqrt{10},x=-2\sqrt{10}$