Solve V^2=1024

$$V ^ { 2 } = 1024$$

Solve for V

$$V=32$$

$$V=-32$$

Steps Using Difference of Squares

Subtract 1024 from both sides.

$$V^{2}-1024=0$$

Consider V^{2}-1024. Rewrite V^{2}-1024 as V^{2}-32^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(V-32\right)\left(V+32\right)=0$$

To find equation solutions, solve V-32=0 and V+32=0.

$$V=32 V=-32$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$V=32 V=-32$$

Steps Using the Quadratic Formula

Subtract 1024 from both sides.

$$V^{2}-1024=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1024 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$V=\frac{0±\sqrt{0^{2}-4\left(-1024\right)}}{2}$$

Square 0.

$$V=\frac{0±\sqrt{-4\left(-1024\right)}}{2}$$

Multiply -4 times -1024.

$$V=\frac{0±\sqrt{4096}}{2}$$

Take the square root of 4096.

$$V=\frac{0±64}{2}$$

Now solve the equation V=\frac{0±64}{2} when ± is plus. Divide 64 by 2.

$$V=32$$

Now solve the equation V=\frac{0±64}{2} when ± is minus. Divide -64 by 2.

$$V=-32$$

The equation is now solved.

$$V=32 V=-32$$