Question

Which number(s) is(are) equal to half its (their) square?

Answer 1

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.