Solve 1^3/1^2=18^3/x^2

$$\frac{ { 1 }^{ 3 } }{ { 1 }^{ 2 } } = \frac{ { 18 }^{ 3 } }{ { x }^{ 2 } }$$

Solve for x

$$x=54\sqrt{2}\approx 76.367532368$$

$$x=-54\sqrt{2}\approx -76.367532368$$

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 x^{2}.

$$x^{2}\times 1^{3}=18^{3}$$

Calculate 1 to the power of 3 and get 1.

$$x^{2}\times 1=18^{3}$$

Calculate 18 to the power of 3 and get 5832.

$$x^{2}\times 1=5832$$

Divide both sides by 1.

$$x^{2}=5832$$

Take the square root of both sides of the equation.

$$x=54\sqrt{2} x=-54\sqrt{2}$$

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 x^{2}.

$$x^{2}\times 1^{3}=18^{3}$$

Calculate 1 to the power of 3 and get 1.

$$x^{2}\times 1=18^{3}$$

Calculate 18 to the power of 3 and get 5832.

$$x^{2}\times 1=5832$$

Subtract 5832 from both sides.

$$x^{2}\times 1-5832=0$$

Reorder the terms.

$$x^{2}-5832=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5832 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5832\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5832\right)}}{2}$$

Multiply -4 times -5832.

$$x=\frac{0±\sqrt{23328}}{2}$$

Take the square root of 23328.

$$x=\frac{0±108\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±108\sqrt{2}}{2} when ± is plus.

$$x=54\sqrt{2}$$

Now solve the equation x=\frac{0±108\sqrt{2}}{2} when ± is minus.

$$x=-54\sqrt{2}$$

The equation is now solved.

$$x=54\sqrt{2} x=-54\sqrt{2}$$