Solve 2(1/x)=48(x)1/60

$$2 ( \frac { 1 } { x } ) = 48 ( x ) \frac { 1 } { 60 }$$

Solve for x

$$x = \frac{\sqrt{10}}{2} \approx 1.58113883$$

$$x = -\frac{\sqrt{10}}{2} \approx -1.58113883$$

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 60x, the least common multiple of x,60.

$$2\times 60\times 1=48x\times \frac{1}{60}\times 60x$$

Multiply 2 and 60 to get 120.

$$120\times 1=48x\times \frac{1}{60}\times 60x$$

Multiply 120 and 1 to get 120.

$$120=48x\times \frac{1}{60}\times 60x$$

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

$$120=48x^{2}\times \frac{1}{60}\times 60$$

Multiply 48 and \frac{1}{60} to get \frac{48}{60}.

$$120=\frac{48}{60}x^{2}\times 60$$

Reduce the fraction \frac{48}{60} to lowest terms by extracting and canceling out 12.

$$120=\frac{4}{5}x^{2}\times 60$$

Express \frac{4}{5}\times 60 as a single fraction.

$$120=\frac{4\times 60}{5}x^{2}$$

Multiply 4 and 60 to get 240.

$$120=\frac{240}{5}x^{2}$$

Divide 240 by 5 to get 48.

$$120=48x^{2}$$

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

$$48x^{2}=120$$

Divide both sides by 48.

$$x^{2}=\frac{120}{48}$$

Reduce the fraction \frac{120}{48} to lowest terms by extracting and canceling out 24.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$

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 60x, the least common multiple of x,60.

$$2\times 60\times 1=48x\times \frac{1}{60}\times 60x$$

Multiply 2 and 60 to get 120.

$$120\times 1=48x\times \frac{1}{60}\times 60x$$

Multiply 120 and 1 to get 120.

$$120=48x\times \frac{1}{60}\times 60x$$

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

$$120=48x^{2}\times \frac{1}{60}\times 60$$

Multiply 48 and \frac{1}{60} to get \frac{48}{60}.

$$120=\frac{48}{60}x^{2}\times 60$$

Reduce the fraction \frac{48}{60} to lowest terms by extracting and canceling out 12.

$$120=\frac{4}{5}x^{2}\times 60$$

Express \frac{4}{5}\times 60 as a single fraction.

$$120=\frac{4\times 60}{5}x^{2}$$

Multiply 4 and 60 to get 240.

$$120=\frac{240}{5}x^{2}$$

Divide 240 by 5 to get 48.

$$120=48x^{2}$$

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

$$48x^{2}=120$$

Subtract 120 from both sides.

$$48x^{2}-120=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 48 for a, 0 for b, and -120 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 48\left(-120\right)}}{2\times 48}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 48\left(-120\right)}}{2\times 48}$$

Multiply -4 times 48.

$$x=\frac{0±\sqrt{-192\left(-120\right)}}{2\times 48}$$

Multiply -192 times -120.

$$x=\frac{0±\sqrt{23040}}{2\times 48}$$

Take the square root of 23040.

$$x=\frac{0±48\sqrt{10}}{2\times 48}$$

Multiply 2 times 48.

$$x=\frac{0±48\sqrt{10}}{96}$$

Now solve the equation x=\frac{0±48\sqrt{10}}{96} when ± is plus.

$$x=\frac{\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±48\sqrt{10}}{96} when ± is minus.

$$x=-\frac{\sqrt{10}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$