Solve pix^2-4=1/8

$$\pi x ^ { 2 } - 4 = \frac { 1 } { 8 }$$

Solve for x

$$x = \frac{\sqrt{\frac{66}{\pi}}}{4} \approx 1.145874461$$

$$x = -\frac{\sqrt{\frac{66}{\pi}}}{4} \approx -1.145874461$$

Steps by Finding Square Root

Add 4 to both sides.

$$\pi x^{2}=\frac{1}{8}+4$$

Add \frac{1}{8} and 4 to get \frac{33}{8}.

$$\pi x^{2}=\frac{33}{8}$$

Divide both sides by \pi .

$$\frac{\pi x^{2}}{\pi }=\frac{\frac{33}{8}}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$x^{2}=\frac{\frac{33}{8}}{\pi }$$

Divide \frac{33}{8} by \pi .

$$x^{2}=\frac{33}{8\pi }$$

Take the square root of both sides of the equation.

$$x=\frac{33}{2\sqrt{66\pi }} x=-\frac{33}{2\sqrt{66\pi }}$$

Steps Using the Quadratic Formula

Subtract \frac{1}{8} from both sides.

$$\pi x^{2}-4-\frac{1}{8}=0$$

Subtract \frac{1}{8} from -4 to get -\frac{33}{8}.

$$\pi x^{2}-\frac{33}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -\frac{33}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\pi \left(-\frac{33}{8}\right)}}{2\pi }$$

Square 0.

$$x=\frac{0±\sqrt{-4\pi \left(-\frac{33}{8}\right)}}{2\pi }$$

Multiply -4 times \pi .

$$x=\frac{0±\sqrt{\left(-4\pi \right)\left(-\frac{33}{8}\right)}}{2\pi }$$

Multiply -4\pi times -\frac{33}{8}.

$$x=\frac{0±\sqrt{\frac{33\pi }{2}}}{2\pi }$$

Take the square root of \frac{33\pi }{2}.

$$x=\frac{0±\frac{\sqrt{66\pi }}{2}}{2\pi }$$

Now solve the equation x=\frac{0±\frac{\sqrt{66\pi }}{2}}{2\pi } when ± is plus.

$$x=\frac{33}{2\sqrt{66\pi }}$$

Now solve the equation x=\frac{0±\frac{\sqrt{66\pi }}{2}}{2\pi } when ± is minus.

$$x=-\frac{33}{2\sqrt{66\pi }}$$

The equation is now solved.

$$x=\frac{33}{2\sqrt{66\pi }} x=-\frac{33}{2\sqrt{66\pi }}$$