Solve r^2=441

$$r ^ { 2 } = 441$$

Solve for r

$$r=21$$

$$r=-21$$

Steps Using Difference of Squares

Subtract 441 from both sides.

$$r^{2}-441=0$$

Consider r^{2}-441. Rewrite r^{2}-441 as r^{2}-21^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-21\right)\left(r+21\right)=0$$

To find equation solutions, solve r-21=0 and r+21=0.

$$r=21 r=-21$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$r=21 r=-21$$

Steps Using the Quadratic Formula

Subtract 441 from both sides.

$$r^{2}-441=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -441 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-441\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-441\right)}}{2}$$

Multiply -4 times -441.

$$r=\frac{0±\sqrt{1764}}{2}$$

Take the square root of 1764.

$$r=\frac{0±42}{2}$$

Now solve the equation r=\frac{0±42}{2} when ± is plus. Divide 42 by 2.

$$r=21$$

Now solve the equation r=\frac{0±42}{2} when ± is minus. Divide -42 by 2.

$$r=-21$$

The equation is now solved.

$$r=21 r=-21$$