Solve (pi)*(d/2)^2=484pi

$$( \pi ) \times ( \frac { d } { 2 } ) ^ { 2 } = 484 \pi$$

Solve for d

$$d=44$$

$$d=-44$$

Steps Using Difference of Squares

Cancel out \pi on both sides.

$$\left(\frac{d}{2}\right)^{2}=484$$

To raise \frac{d}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{d^{2}}{2^{2}}=484$$

Calculate 2 to the power of 2 and get 4.

$$\frac{d^{2}}{4}=484$$

Subtract 484 from both sides.

$$\frac{d^{2}}{4}-484=0$$

Multiply both sides of the equation by 4.

$$d^{2}-1936=0$$

Consider d^{2}-1936. Rewrite d^{2}-1936 as d^{2}-44^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(d-44\right)\left(d+44\right)=0$$

To find equation solutions, solve d-44=0 and d+44=0.

$$d=44 d=-44$$

Steps by Finding Square Root

Cancel out \pi on both sides.

$$\left(\frac{d}{2}\right)^{2}=484$$

To raise \frac{d}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{d^{2}}{2^{2}}=484$$

Calculate 2 to the power of 2 and get 4.

$$\frac{d^{2}}{4}=484$$

Multiply both sides by 4.

$$d^{2}=484\times 4$$

Multiply 484 and 4 to get 1936.

$$d^{2}=1936$$

Take the square root of both sides of the equation.

$$d=44 d=-44$$

Steps Using the Quadratic Formula

Cancel out \pi on both sides.

$$\left(\frac{d}{2}\right)^{2}=484$$

To raise \frac{d}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{d^{2}}{2^{2}}=484$$

Calculate 2 to the power of 2 and get 4.

$$\frac{d^{2}}{4}=484$$

Subtract 484 from both sides.

$$\frac{d^{2}}{4}-484=0$$

Multiply both sides of the equation by 4.

$$d^{2}-1936=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1936 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\left(-1936\right)}}{2}$$

Square 0.

$$d=\frac{0±\sqrt{-4\left(-1936\right)}}{2}$$

Multiply -4 times -1936.

$$d=\frac{0±\sqrt{7744}}{2}$$

Take the square root of 7744.

$$d=\frac{0±88}{2}$$

Now solve the equation d=\frac{0±88}{2} when ± is plus. Divide 88 by 2.

$$d=44$$

Now solve the equation d=\frac{0±88}{2} when ± is minus. Divide -88 by 2.

$$d=-44$$

The equation is now solved.

$$d=44 d=-44$$