Solve x^2=64/100

$$x ^ { 2 } = \frac { 64 } { 100 }$$

Solve for x

$$x=\frac{4}{5}=0.8$$

$$x=-\frac{4}{5}=-0.8$$

Steps Using Difference of Squares

Reduce the fraction \frac{64}{100} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{16}{25}$$

Subtract \frac{16}{25} from both sides.

$$x^{2}-\frac{16}{25}=0$$

Multiply both sides by 25.

$$25x^{2}-16=0$$

Consider 25x^{2}-16. Rewrite 25x^{2}-16 as \left(5x\right)^{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).

$$\left(5x-4\right)\left(5x+4\right)=0$$

To find equation solutions, solve 5x-4=0 and 5x+4=0.

$$x=\frac{4}{5} x=-\frac{4}{5}$$

Steps by Finding Square Root

Reduce the fraction \frac{64}{100} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{4}{5} x=-\frac{4}{5}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{64}{100} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{16}{25}$$

Subtract \frac{16}{25} from both sides.

$$x^{2}-\frac{16}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{25}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{16}{25}\right)}}{2}$$

Multiply -4 times -\frac{16}{25}.

$$x=\frac{0±\sqrt{\frac{64}{25}}}{2}$$

Take the square root of \frac{64}{25}.

$$x=\frac{0±\frac{8}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{8}{5}}{2} when ± is plus.

$$x=\frac{4}{5}$$

Now solve the equation x=\frac{0±\frac{8}{5}}{2} when ± is minus.

$$x=-\frac{4}{5}$$

The equation is now solved.

$$x=\frac{4}{5} x=-\frac{4}{5}$$