Question

Which number(s) is(are) equal to the quarter of its (their) square?

Answer 1

If \(x\) is the number to find, then the quarter of its square is \((1 / 4) x^{2}\).
\(x\) is equal to the quarter of its square hence: \(x=(1 / 4) x^{2}\)
First write the above equation with its right side equal to zero.
\(x-(1 / 4) x^{2}=0\)
\(x(1-(1 / 4) x)=0\), factor \(x\) out
solutions: \(x=0\) and \(x=4\)

Check answers.
1) \(x=0\), quarter of its square is \((1 / 4) 0^{2}=0\). Hence \(x\) and the quarter of its square are equal.

2) \(x=4\), the quarter of its square is \((1 / 4) 4^{2}=4\). Hence \(x\) and the quarter of its square ar. equal.