Solve 0.81=x^2

$$0.81= { x }^{ 2 }$$

Solve for x

$$x=0.9$$

$$x=-0.9$$

Steps Using Difference of Squares

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=0.81$$

Subtract 0.81 from both sides.

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

Consider x^{2}-0.81. Rewrite x^{2}-0.81 as x^{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).

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

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

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

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=0.81$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=0.81$$

Subtract 0.81 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -0.81.

$$x=\frac{0±\sqrt{3.24}}{2}$$

Take the square root of 3.24.

$$x=\frac{0±\frac{9}{5}}{2}$$

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

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

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

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

The equation is now solved.

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