Solve x^2=.16

$${ x }^{ 2 } =.16$$

Solve for x

$$x=0.4$$

$$x=-0.4$$

Steps Using Difference of Squares

Subtract 0.16 from both sides.

$$x^{2}-0.16=0$$

Consider x^{2}-0.16. Rewrite x^{2}-0.16 as x^{2}-\left(\frac{2}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{2}{5}\right)\left(x+\frac{2}{5}\right)=0$$

To find equation solutions, solve x-\frac{2}{5}=0 and x+\frac{2}{5}=0.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

Steps Using the Quadratic Formula

Subtract 0.16 from both sides.

$$x^{2}-0.16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-0.16\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-0.16\right)}}{2}$$

Multiply -4 times -0.16.

$$x=\frac{0±\sqrt{0.64}}{2}$$

Take the square root of 0.64.

$$x=\frac{0±\frac{4}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{4}{5}}{2} when ± is plus.

$$x=\frac{2}{5}$$

Now solve the equation x=\frac{0±\frac{4}{5}}{2} when ± is minus.

$$x=-\frac{2}{5}$$

The equation is now solved.

$$x=\frac{2}{5} x=-\frac{2}{5}$$