Let \(x\) be the number to find. Half its square is \((1 / 2) x^{2}\).

\(x\) is equal to half its square hence: \(x=(1 / 2) x^{2}\)

First write with right side equal to zero.

\[

\begin{aligned}

&x-(1 / 2) x^{2}=0 \\

&x(1-(1 / 2) x)=0, \text { factor }

\end{aligned}

\]

solutions: \(x=0\) and \(x=2\)

Check answers.

1) \(x=0\), half its square is \((1 / 2) 0^{2}=0\). Hence \(x\) and half its square are equal.

2) \(x=2\), half its square is \((1 / 2) 2^{2}=2\). Hence \(x\) and half its square are equal.