Solve 81r^2=49

$$81 r ^ { 2 } = 49$$

Solve for r

$$r=\frac{7}{9}\approx 0.777777778$$

$$r=-\frac{7}{9}\approx -0.777777778$$

Steps Using Difference of Squares

Divide both sides by 81.

$$r^{2}=\frac{49}{81}$$

Subtract \frac{49}{81} from both sides.

$$r^{2}-\frac{49}{81}=0$$

Multiply both sides by 81.

$$81r^{2}-49=0$$

Consider 81r^{2}-49. Rewrite 81r^{2}-49 as \left(9r\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9r-7\right)\left(9r+7\right)=0$$

To find equation solutions, solve 9r-7=0 and 9r+7=0.

$$r=\frac{7}{9} r=-\frac{7}{9}$$

Steps by Finding Square Root

Divide both sides by 81.

$$r^{2}=\frac{49}{81}$$

Take the square root of both sides of the equation.

$$r=\frac{7}{9} r=-\frac{7}{9}$$

Steps Using the Quadratic Formula

Divide both sides by 81.

$$r^{2}=\frac{49}{81}$$

Subtract \frac{49}{81} from both sides.

$$r^{2}-\frac{49}{81}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{49}{81} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{81}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{49}{81}\right)}}{2}$$

Multiply -4 times -\frac{49}{81}.

$$r=\frac{0±\sqrt{\frac{196}{81}}}{2}$$

Take the square root of \frac{196}{81}.

$$r=\frac{0±\frac{14}{9}}{2}$$

Now solve the equation r=\frac{0±\frac{14}{9}}{2} when ± is plus.

$$r=\frac{7}{9}$$

Now solve the equation r=\frac{0±\frac{14}{9}}{2} when ± is minus.

$$r=-\frac{7}{9}$$

The equation is now solved.

$$r=\frac{7}{9} r=-\frac{7}{9}$$