Solve v^2=121

$$v ^ { 2 } = 121$$

Solve for v

$$v=11$$

$$v=-11$$

Steps Using Difference of Squares

Subtract 121 from both sides.

$$v^{2}-121=0$$

Consider v^{2}-121. Rewrite v^{2}-121 as v^{2}-11^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-11\right)\left(v+11\right)=0$$

To find equation solutions, solve v-11=0 and v+11=0.

$$v=11 v=-11$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$v=11 v=-11$$

Steps Using the Quadratic Formula

Subtract 121 from both sides.

$$v^{2}-121=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -121 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-121\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-121\right)}}{2}$$

Multiply -4 times -121.

$$v=\frac{0±\sqrt{484}}{2}$$

Take the square root of 484.

$$v=\frac{0±22}{2}$$

Now solve the equation v=\frac{0±22}{2} when ± is plus. Divide 22 by 2.

$$v=11$$

Now solve the equation v=\frac{0±22}{2} when ± is minus. Divide -22 by 2.

$$v=-11$$

The equation is now solved.

$$v=11 v=-11$$