Solve pix^2=1500

$$\pi x ^ { 2 } = 1500$$

Solve for x

$$x=10\sqrt{\frac{15}{\pi }}\approx 21.850968612$$

$$x=-10\sqrt{\frac{15}{\pi }}\approx -21.850968612$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi x^{2}}{\pi }=\frac{1500}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$x^{2}=\frac{1500}{\pi }$$

Take the square root of both sides of the equation.

$$x=\frac{150}{\sqrt{15\pi }} x=-\frac{150}{\sqrt{15\pi }}$$

Steps Using the Quadratic Formula

Subtract 1500 from both sides.

$$\pi x^{2}-1500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -1500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\pi \left(-1500\right)}}{2\pi }$$

Square 0.

$$x=\frac{0±\sqrt{-4\pi \left(-1500\right)}}{2\pi }$$

Multiply -4 times \pi .

$$x=\frac{0±\sqrt{\left(-4\pi \right)\left(-1500\right)}}{2\pi }$$

Multiply -4\pi times -1500.

$$x=\frac{0±\sqrt{6000\pi }}{2\pi }$$

Take the square root of 6000\pi .

$$x=\frac{0±20\sqrt{15\pi }}{2\pi }$$

Now solve the equation x=\frac{0±20\sqrt{15\pi }}{2\pi } when ± is plus.

$$x=\frac{150}{\sqrt{15\pi }}$$

Now solve the equation x=\frac{0±20\sqrt{15\pi }}{2\pi } when ± is minus.

$$x=-\frac{150}{\sqrt{15\pi }}$$

The equation is now solved.

$$x=\frac{150}{\sqrt{15\pi }} x=-\frac{150}{\sqrt{15\pi }}$$