Solve pix^2=1/2*16*12

$$\pi x ^ { 2 } = \frac { 1 } { 2 } \times 16 \times 12$$

Solve for x

$$x=4\sqrt{\frac{6}{\pi }}\approx 5.527906392$$

$$x=-4\sqrt{\frac{6}{\pi }}\approx -5.527906392$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 16 to get 8.

$$\pi x^{2}=8\times 12$$

Multiply 8 and 12 to get 96.

$$\pi x^{2}=96$$

Divide both sides by \pi .

$$\frac{\pi x^{2}}{\pi }=\frac{96}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$x^{2}=\frac{96}{\pi }$$

Take the square root of both sides of the equation.

$$x=\frac{24}{\sqrt{6\pi }} x=-\frac{24}{\sqrt{6\pi }}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 16 to get 8.

$$\pi x^{2}=8\times 12$$

Multiply 8 and 12 to get 96.

$$\pi x^{2}=96$$

Subtract 96 from both sides.

$$\pi x^{2}-96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\pi \left(-96\right)}}{2\pi }$$

Square 0.

$$x=\frac{0±\sqrt{-4\pi \left(-96\right)}}{2\pi }$$

Multiply -4 times \pi .

$$x=\frac{0±\sqrt{\left(-4\pi \right)\left(-96\right)}}{2\pi }$$

Multiply -4\pi times -96.

$$x=\frac{0±\sqrt{384\pi }}{2\pi }$$

Take the square root of 384\pi .

$$x=\frac{0±8\sqrt{6\pi }}{2\pi }$$

Now solve the equation x=\frac{0±8\sqrt{6\pi }}{2\pi } when ± is plus.

$$x=\frac{24}{\sqrt{6\pi }}$$

Now solve the equation x=\frac{0±8\sqrt{6\pi }}{2\pi } when ± is minus.

$$x=-\frac{24}{\sqrt{6\pi }}$$

The equation is now solved.

$$x=\frac{24}{\sqrt{6\pi }} x=-\frac{24}{\sqrt{6\pi }}$$