Solve (720x)x=2592

$$(720x)x = 2592$$

Solve for x

$$x = \frac{3 \sqrt{10}}{5} \approx 1.897366596$$

$$x = -\frac{3 \sqrt{10}}{5} \approx -1.897366596$$

Steps by Finding Square Root

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

$$720x^{2}=2592$$

Divide both sides by 720.

$$x^{2}=\frac{2592}{720}$$

Reduce the fraction \frac{2592}{720} to lowest terms by extracting and canceling out 144.

$$x^{2}=\frac{18}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{5} x=-\frac{3\sqrt{10}}{5}$$

Steps Using the Quadratic Formula

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

$$720x^{2}=2592$$

Subtract 2592 from both sides.

$$720x^{2}-2592=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 720 for a, 0 for b, and -2592 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 720\left(-2592\right)}}{2\times 720}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 720\left(-2592\right)}}{2\times 720}$$

Multiply -4 times 720.

$$x=\frac{0±\sqrt{-2880\left(-2592\right)}}{2\times 720}$$

Multiply -2880 times -2592.

$$x=\frac{0±\sqrt{7464960}}{2\times 720}$$

Take the square root of 7464960.

$$x=\frac{0±864\sqrt{10}}{2\times 720}$$

Multiply 2 times 720.

$$x=\frac{0±864\sqrt{10}}{1440}$$

Now solve the equation x=\frac{0±864\sqrt{10}}{1440} when ± is plus.

$$x=\frac{3\sqrt{10}}{5}$$

Now solve the equation x=\frac{0±864\sqrt{10}}{1440} when ± is minus.

$$x=-\frac{3\sqrt{10}}{5}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{5} x=-\frac{3\sqrt{10}}{5}$$