Solve (720x)x=259.2

$$(720x)x = 259.2$$

Solve for x

$$x=0.6$$

$$x=-0.6$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$720x^{2}=259.2$$

Divide both sides by 720.

$$x^{2}=\frac{259.2}{720}$$

Expand \frac{259.2}{720} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{2592}{7200}$$

Reduce the fraction \frac{2592}{7200} to lowest terms by extracting and canceling out 288.

$$x^{2}=\frac{9}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{5} x=-\frac{3}{5}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$720x^{2}=259.2$$

Subtract 259.2 from both sides.

$$720x^{2}-259.2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 720 for a, 0 for b, and -259.2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 720\left(-259.2\right)}}{2\times 720}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 720\left(-259.2\right)}}{2\times 720}$$

Multiply -4 times 720.

$$x=\frac{0±\sqrt{-2880\left(-259.2\right)}}{2\times 720}$$

Multiply -2880 times -259.2.

$$x=\frac{0±\sqrt{746496}}{2\times 720}$$

Take the square root of 746496.

$$x=\frac{0±864}{2\times 720}$$

Multiply 2 times 720.

$$x=\frac{0±864}{1440}$$

Now solve the equation x=\frac{0±864}{1440} when ± is plus. Reduce the fraction \frac{864}{1440} to lowest terms by extracting and canceling out 288.

$$x=\frac{3}{5}$$

Now solve the equation x=\frac{0±864}{1440} when ± is minus. Reduce the fraction \frac{-864}{1440} to lowest terms by extracting and canceling out 288.

$$x=-\frac{3}{5}$$

The equation is now solved.

$$x=\frac{3}{5} x=-\frac{3}{5}$$