Solve v^2=25

$$v ^ { 2 } = 25$$

Solve for v

$$v=5$$

$$v=-5$$

Steps Using Difference of Squares

Subtract 25 from both sides.

$$v^{2}-25=0$$

Consider v^{2}-25. Rewrite v^{2}-25 as v^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-5\right)\left(v+5\right)=0$$

To find equation solutions, solve v-5=0 and v+5=0.

$$v=5 v=-5$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$v=5 v=-5$$

Steps Using the Quadratic Formula

Subtract 25 from both sides.

$$v^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

Multiply -4 times -25.

$$v=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$v=\frac{0±10}{2}$$

Now solve the equation v=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$v=5$$

Now solve the equation v=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$v=-5$$

The equation is now solved.

$$v=5 v=-5$$