Solve 1/x^2=6^5

$$\frac{ 1 }{ { x }^{ 2 } } = { 6 }^{ 5 }$$

Solve for x

$$x=\frac{\sqrt{6}}{216}\approx 0.01134023$$

$$x=-\frac{\sqrt{6}}{216}\approx -0.01134023$$

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}.

$$1=x^{2}\times 6^{5}$$

Calculate 6 to the power of 5 and get 7776.

$$1=x^{2}\times 7776$$

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

$$x^{2}\times 7776=1$$

Divide both sides by 7776.

$$x^{2}=\frac{1}{7776}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{216} x=-\frac{\sqrt{6}}{216}$$

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}.

$$1=x^{2}\times 6^{5}$$

Calculate 6 to the power of 5 and get 7776.

$$1=x^{2}\times 7776$$

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

$$x^{2}\times 7776=1$$

Subtract 1 from both sides.

$$x^{2}\times 7776-1=0$$

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.

$$7776x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7776 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7776\left(-1\right)}}{2\times 7776}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7776\left(-1\right)}}{2\times 7776}$$

Multiply -4 times 7776.

$$x=\frac{0±\sqrt{-31104\left(-1\right)}}{2\times 7776}$$

Multiply -31104 times -1.

$$x=\frac{0±\sqrt{31104}}{2\times 7776}$$

Take the square root of 31104.

$$x=\frac{0±72\sqrt{6}}{2\times 7776}$$

Multiply 2 times 7776.

$$x=\frac{0±72\sqrt{6}}{15552}$$

Now solve the equation x=\frac{0±72\sqrt{6}}{15552} when ± is plus.

$$x=\frac{\sqrt{6}}{216}$$

Now solve the equation x=\frac{0±72\sqrt{6}}{15552} when ± is minus.

$$x=-\frac{\sqrt{6}}{216}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{216} x=-\frac{\sqrt{6}}{216}$$