Solve x^2*pi=15

$$x ^ { 2 } \times \pi = 15$$

Solve for x

$$x=\sqrt{\frac{15}{\pi }}\approx 2.185096861$$

$$x=-\sqrt{\frac{15}{\pi }}\approx -2.185096861$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi x^{2}}{\pi }=\frac{15}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$x^{2}=\frac{15}{\pi }$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 15 from both sides.

$$x^{2}\pi -15=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\pi x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\pi \left(-15\right)}}{2\pi }$$

Square 0.

$$x=\frac{0±\sqrt{-4\pi \left(-15\right)}}{2\pi }$$

Multiply -4 times \pi .

$$x=\frac{0±\sqrt{\left(-4\pi \right)\left(-15\right)}}{2\pi }$$

Multiply -4\pi times -15.

$$x=\frac{0±\sqrt{60\pi }}{2\pi }$$

Take the square root of 60\pi .

$$x=\frac{0±2\sqrt{15\pi }}{2\pi }$$

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

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

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

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

The equation is now solved.

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