Solve p^2=0.81

$$p ^ { 2 } = 0.81$$

Solve for p

$$p=0.9$$

$$p=-0.9$$

Steps Using Difference of Squares

Subtract 0.81 from both sides.

$$p^{2}-0.81=0$$

Consider p^{2}-0.81. Rewrite p^{2}-0.81 as p^{2}-\left(\frac{9}{10}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(p-\frac{9}{10}\right)\left(p+\frac{9}{10}\right)=0$$

To find equation solutions, solve p-\frac{9}{10}=0 and p+\frac{9}{10}=0.

$$p=\frac{9}{10} p=-\frac{9}{10}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$p=\frac{9}{10} p=-\frac{9}{10}$$

Steps Using the Quadratic Formula

Subtract 0.81 from both sides.

$$p^{2}-0.81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-0.81\right)}}{2}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-0.81\right)}}{2}$$

Multiply -4 times -0.81.

$$p=\frac{0±\sqrt{3.24}}{2}$$

Take the square root of 3.24.

$$p=\frac{0±\frac{9}{5}}{2}$$

Now solve the equation p=\frac{0±\frac{9}{5}}{2} when ± is plus.

$$p=\frac{9}{10}$$

Now solve the equation p=\frac{0±\frac{9}{5}}{2} when ± is minus.

$$p=-\frac{9}{10}$$

The equation is now solved.

$$p=\frac{9}{10} p=-\frac{9}{10}$$