Solve x/9=3/x

$$\frac { x } { 9 } = \frac { 3 } { x }$$

Solve for x

$$x=3\sqrt{3}\approx 5.196152423$$

$$x=-3\sqrt{3}\approx -5.196152423$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x, the least common multiple of 9,x.

$$xx=9\times 3$$

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

$$x^{2}=9\times 3$$

Multiply 9 and 3 to get 27.

$$x^{2}=27$$

Take the square root of both sides of the equation.

$$x=3\sqrt{3} x=-3\sqrt{3}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x, the least common multiple of 9,x.

$$xx=9\times 3$$

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

$$x^{2}=9\times 3$$

Multiply 9 and 3 to get 27.

$$x^{2}=27$$

Subtract 27 from both sides.

$$x^{2}-27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-27\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-27\right)}}{2}$$

Multiply -4 times -27.

$$x=\frac{0±\sqrt{108}}{2}$$

Take the square root of 108.

$$x=\frac{0±6\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{3}}{2} when ± is plus.

$$x=3\sqrt{3}$$

Now solve the equation x=\frac{0±6\sqrt{3}}{2} when ± is minus.

$$x=-3\sqrt{3}$$

The equation is now solved.

$$x=3\sqrt{3} x=-3\sqrt{3}$$