Solve v^2-36=0

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

Solve for v

$$v=6$$

$$v=-6$$

Steps Using Difference of Squares

Consider v^{2}-36. Rewrite v^{2}-36 as v^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

$$v=6 v=-6$$

Steps by Finding Square Root

Add 36 to both sides. Anything plus zero gives itself.

$$v^{2}=36$$

Take the square root of both sides of the equation.

$$v=6 v=-6$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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

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

Square 0.

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

Multiply -4 times -36.

$$v=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$v=\frac{0±12}{2}$$

Now solve the equation v=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$v=6$$

Now solve the equation v=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$v=-6$$

The equation is now solved.

$$v=6 v=-6$$