Solve A^2=16

$$A ^ { 2 } = 16$$

Solve for A

$$A=4$$

$$A=-4$$

Steps Using Difference of Squares

Subtract 16 from both sides.

$$A^{2}-16=0$$

Consider A^{2}-16. Rewrite A^{2}-16 as A^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(A-4\right)\left(A+4\right)=0$$

To find equation solutions, solve A-4=0 and A+4=0.

$$A=4 A=-4$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$A=4 A=-4$$

Steps Using the Quadratic Formula

Subtract 16 from both sides.

$$A^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square 0.

$$A=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$A=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$A=\frac{0±8}{2}$$

Now solve the equation A=\frac{0±8}{2} when ± is plus. Divide 8 by 2.

$$A=4$$

Now solve the equation A=\frac{0±8}{2} when ± is minus. Divide -8 by 2.

$$A=-4$$

The equation is now solved.

$$A=4 A=-4$$