Solve 1/5x^2-16/5=0

$$\frac { 1 } { 5 } x ^ { 2 } - \frac { 16 } { 5 } = 0$$

Solve for x

$$x=4$$

$$x=-4$$

Steps Using Difference of Squares

Multiply both sides by 5.

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

Consider x^{2}-16. Rewrite x^{2}-16 as x^{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).

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

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

$$x=4 x=-4$$

Steps by Finding Square Root

Add \frac{16}{5} to both sides. Anything plus zero gives itself.

$$\frac{1}{5}x^{2}=\frac{16}{5}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x^{2}=\frac{16}{5}\times 5$$

Multiply \frac{16}{5} and 5 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{1}{5}x^{2}-\frac{16}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{5} for a, 0 for b, and -\frac{16}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{5}\left(-\frac{16}{5}\right)}}{2\times \frac{1}{5}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{5}\left(-\frac{16}{5}\right)}}{2\times \frac{1}{5}}$$

Multiply -4 times \frac{1}{5}.

$$x=\frac{0±\sqrt{-\frac{4}{5}\left(-\frac{16}{5}\right)}}{2\times \frac{1}{5}}$$

Multiply -\frac{4}{5} times -\frac{16}{5} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{64}{25}}}{2\times \frac{1}{5}}$$

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

$$x=\frac{0±\frac{8}{5}}{2\times \frac{1}{5}}$$

Multiply 2 times \frac{1}{5}.

$$x=\frac{0±\frac{8}{5}}{\frac{2}{5}}$$

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

$$x=4$$

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

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$