Solve 150/360pi(x^2)=60pi

$$\frac{ 150 }{ 360 } \pi ( { x }^{ 2 } )=60 \pi$$

Solve for x

$$x=12$$

$$x=-12$$

Steps Using Difference of Squares

Cancel out \pi on both sides.

$$\frac{150}{360}x^{2}=60$$

Reduce the fraction \frac{150}{360} to lowest terms by extracting and canceling out 30.

$$\frac{5}{12}x^{2}=60$$

Subtract 60 from both sides.

$$\frac{5}{12}x^{2}-60=0$$

Divide both sides by \frac{5}{12}.

$$x^{2}-144=0$$

Consider x^{2}-144. Rewrite x^{2}-144 as x^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-12\right)\left(x+12\right)=0$$

To find equation solutions, solve x-12=0 and x+12=0.

$$x=12 x=-12$$

Steps by Finding Square Root

Cancel out \pi on both sides.

$$\frac{150}{360}x^{2}=60$$

Reduce the fraction \frac{150}{360} to lowest terms by extracting and canceling out 30.

$$\frac{5}{12}x^{2}=60$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x^{2}=60\times \frac{12}{5}$$

Multiply 60 and \frac{12}{5} to get 144.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

Cancel out \pi on both sides.

$$\frac{150}{360}x^{2}=60$$

Reduce the fraction \frac{150}{360} to lowest terms by extracting and canceling out 30.

$$\frac{5}{12}x^{2}=60$$

Subtract 60 from both sides.

$$\frac{5}{12}x^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{5}{12} for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{5}{12}\left(-60\right)}}{2\times \frac{5}{12}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{5}{12}\left(-60\right)}}{2\times \frac{5}{12}}$$

Multiply -4 times \frac{5}{12}.

$$x=\frac{0±\sqrt{-\frac{5}{3}\left(-60\right)}}{2\times \frac{5}{12}}$$

Multiply -\frac{5}{3} times -60.

$$x=\frac{0±\sqrt{100}}{2\times \frac{5}{12}}$$

Take the square root of 100.

$$x=\frac{0±10}{2\times \frac{5}{12}}$$

Multiply 2 times \frac{5}{12}.

$$x=\frac{0±10}{\frac{5}{6}}$$

Now solve the equation x=\frac{0±10}{\frac{5}{6}} when ± is plus. Divide 10 by \frac{5}{6} by multiplying 10 by the reciprocal of \frac{5}{6}.

$$x=12$$

Now solve the equation x=\frac{0±10}{\frac{5}{6}} when ± is minus. Divide -10 by \frac{5}{6} by multiplying -10 by the reciprocal of \frac{5}{6}.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$