Solve (36*3/x)^2=12

$$( \frac { 36 \times 3 } { x } ) ^ { 2 } = 12$$

Solve for x

$$x=-18\sqrt{3}\approx -31.176914536$$

$$x=18\sqrt{3}\approx 31.176914536$$

Steps by Finding Square Root

Multiply 36 and 3 to get 108.

$$\left(\frac{108}{x}\right)^{2}=12$$

To raise \frac{108}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{108^{2}}{x^{2}}=12$$

Calculate 108 to the power of 2 and get 11664.

$$\frac{11664}{x^{2}}=12$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$11664=12x^{2}$$

Divide both sides by 12.

$$\frac{11664}{12}=x^{2}$$

Divide 11664 by 12 to get 972.

$$972=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=972$$

Take the square root of both sides of the equation.

$$x=18\sqrt{3} x=-18\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply 36 and 3 to get 108.

$$\left(\frac{108}{x}\right)^{2}=12$$

To raise \frac{108}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{108^{2}}{x^{2}}=12$$

Calculate 108 to the power of 2 and get 11664.

$$\frac{11664}{x^{2}}=12$$

Subtract 12 from both sides.

$$\frac{11664}{x^{2}}-12=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{x^{2}}{x^{2}}.

$$\frac{11664}{x^{2}}-\frac{12x^{2}}{x^{2}}=0$$

Since \frac{11664}{x^{2}} and \frac{12x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11664-12x^{2}}{x^{2}}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$11664-12x^{2}=0$$

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.

$$-12x^{2}+11664=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 0 for b, and 11664 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 11664}}{2\left(-12\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 11664}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48\times 11664}}{2\left(-12\right)}$$

Multiply 48 times 11664.

$$x=\frac{0±\sqrt{559872}}{2\left(-12\right)}$$

Take the square root of 559872.

$$x=\frac{0±432\sqrt{3}}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{0±432\sqrt{3}}{-24}$$

Now solve the equation x=\frac{0±432\sqrt{3}}{-24} when ± is plus.

$$x=-18\sqrt{3}$$

Now solve the equation x=\frac{0±432\sqrt{3}}{-24} when ± is minus.

$$x=18\sqrt{3}$$

The equation is now solved.

$$x=-18\sqrt{3} x=18\sqrt{3}$$