Solve 36v^2=49

$$36 v ^ { 2 } = 49$$

Solve for v

$$v = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$v = -\frac{7}{6} = -1\frac{1}{6} \approx -1.166666667$$

Steps Using Difference of Squares

Divide both sides by 36.

$$v^{2}=\frac{49}{36}$$

Subtract \frac{49}{36} from both sides.

$$v^{2}-\frac{49}{36}=0$$

Multiply both sides by 36.

$$36v^{2}-49=0$$

Consider 36v^{2}-49. Rewrite 36v^{2}-49 as \left(6v\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).

$$\left(6v-7\right)\left(6v+7\right)=0$$

To find equation solutions, solve 6v-7=0 and 6v+7=0.

$$v=\frac{7}{6} v=-\frac{7}{6}$$

Steps by Finding Square Root

Divide both sides by 36.

$$v^{2}=\frac{49}{36}$$

Take the square root of both sides of the equation.

$$v=\frac{7}{6} v=-\frac{7}{6}$$

Steps Using the Quadratic Formula

Divide both sides by 36.

$$v^{2}=\frac{49}{36}$$

Subtract \frac{49}{36} from both sides.

$$v^{2}-\frac{49}{36}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{49}{36} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{36}\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-\frac{49}{36}\right)}}{2}$$

Multiply -4 times -\frac{49}{36}.

$$v=\frac{0±\sqrt{\frac{49}{9}}}{2}$$

Take the square root of \frac{49}{9}.

$$v=\frac{0±\frac{7}{3}}{2}$$

Now solve the equation v=\frac{0±\frac{7}{3}}{2} when ± is plus.

$$v=\frac{7}{6}$$

Now solve the equation v=\frac{0±\frac{7}{3}}{2} when ± is minus.

$$v=-\frac{7}{6}$$

The equation is now solved.

$$v=\frac{7}{6} v=-\frac{7}{6}$$