Solve a^2=81

$$a ^ { 2 } = 81$$

Solve for a

$$a=9$$

$$a=-9$$

Steps Using Difference of Squares

Subtract 81 from both sides.

$$a^{2}-81=0$$

Consider a^{2}-81. Rewrite a^{2}-81 as a^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-9\right)\left(a+9\right)=0$$

To find equation solutions, solve a-9=0 and a+9=0.

$$a=9 a=-9$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$a=9 a=-9$$

Steps Using the Quadratic Formula

Subtract 81 from both sides.

$$a^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$a=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$a=\frac{0±18}{2}$$

Now solve the equation a=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$a=9$$

Now solve the equation a=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$a=-9$$

The equation is now solved.

$$a=9 a=-9$$