Solve 15625x^2=100

$$15625 x ^ { 2 } = 100$$

Solve for x

$$x=\frac{2}{25}=0.08$$

$$x=-\frac{2}{25}=-0.08$$

Steps Using Difference of Squares

Divide both sides by 15625.

$$x^{2}=\frac{100}{15625}$$

Reduce the fraction \frac{100}{15625} to lowest terms by extracting and canceling out 25.

$$x^{2}=\frac{4}{625}$$

Subtract \frac{4}{625} from both sides.

$$x^{2}-\frac{4}{625}=0$$

Multiply both sides by 625.

$$625x^{2}-4=0$$

Consider 625x^{2}-4. Rewrite 625x^{2}-4 as \left(25x\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(25x-2\right)\left(25x+2\right)=0$$

To find equation solutions, solve 25x-2=0 and 25x+2=0.

$$x=\frac{2}{25} x=-\frac{2}{25}$$

Steps by Finding Square Root

Divide both sides by 15625.

$$x^{2}=\frac{100}{15625}$$

Reduce the fraction \frac{100}{15625} to lowest terms by extracting and canceling out 25.

$$x^{2}=\frac{4}{625}$$

Take the square root of both sides of the equation.

$$x=\frac{2}{25} x=-\frac{2}{25}$$

Steps Using the Quadratic Formula

Divide both sides by 15625.

$$x^{2}=\frac{100}{15625}$$

Reduce the fraction \frac{100}{15625} to lowest terms by extracting and canceling out 25.

$$x^{2}=\frac{4}{625}$$

Subtract \frac{4}{625} from both sides.

$$x^{2}-\frac{4}{625}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{4}{625} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{625}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{4}{625}\right)}}{2}$$

Multiply -4 times -\frac{4}{625}.

$$x=\frac{0±\sqrt{\frac{16}{625}}}{2}$$

Take the square root of \frac{16}{625}.

$$x=\frac{0±\frac{4}{25}}{2}$$

Now solve the equation x=\frac{0±\frac{4}{25}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{4}{25}}{2} when ± is minus.

$$x=-\frac{2}{25}$$

The equation is now solved.

$$x=\frac{2}{25} x=-\frac{2}{25}$$