Solve x=left(xpiright)^2

$$x= { \left(x \pi \right) }^{ 2 }$$

Solve for x

$$x=\frac{1}{\pi ^{2}}\approx 0.101321184$$

$$x=0$$

Steps Using Factoring

Expand \left(x\pi \right)^{2}.

$$x=x^{2}\pi ^{2}$$

Subtract x^{2}\pi ^{2} from both sides.

$$x-x^{2}\pi ^{2}=0$$

Reorder the terms.

$$-\pi ^{2}x^{2}+x=0$$

Factor out x.

$$x\left(-\pi ^{2}x+1\right)=0$$

To find equation solutions, solve x=0 and -\pi ^{2}x+1=0.

$$x=0 x=\frac{1}{\pi ^{2}}$$