Solve 22=r^2+21

$$22 = r ^ { 2 } + 21$$

Solve for r

$$r=1$$

$$r=-1$$

Steps Using Difference of Squares

Swap sides so that all variable terms are on the left hand side.

$$r^{2}+21=22$$

Subtract 22 from both sides.

$$r^{2}+21-22=0$$

Subtract 22 from 21 to get -1.

$$r^{2}-1=0$$

Consider r^{2}-1. Rewrite r^{2}-1 as r^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-1\right)\left(r+1\right)=0$$

To find equation solutions, solve r-1=0 and r+1=0.

$$r=1 r=-1$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$r^{2}+21=22$$

Subtract 21 from both sides.

$$r^{2}=22-21$$

Subtract 21 from 22 to get 1.

$$r^{2}=1$$

Take the square root of both sides of the equation.

$$r=1 r=-1$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$r^{2}+21=22$$

Subtract 22 from both sides.

$$r^{2}+21-22=0$$

Subtract 22 from 21 to get -1.

$$r^{2}-1=0$$

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

$$r=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

Multiply -4 times -1.

$$r=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$r=\frac{0±2}{2}$$

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

$$r=1$$

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

$$r=-1$$

The equation is now solved.

$$r=1 r=-1$$