Solve 74/x^2=5

$$\frac{ 74 }{ { x }^{ 2 } } =5$$

Solve for x

$$x = \frac{\sqrt{370}}{5} \approx 3.847076812$$

$$x = -\frac{\sqrt{370}}{5} \approx -3.847076812$$

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}.

$$74=5x^{2}$$

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

$$5x^{2}=74$$

Divide both sides by 5.

$$x^{2}=\frac{74}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{370}}{5} x=-\frac{\sqrt{370}}{5}$$

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}.

$$74=5x^{2}$$

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

$$5x^{2}=74$$

Subtract 74 from both sides.

$$5x^{2}-74=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -74 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-74\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-74\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-74\right)}}{2\times 5}$$

Multiply -20 times -74.

$$x=\frac{0±\sqrt{1480}}{2\times 5}$$

Take the square root of 1480.

$$x=\frac{0±2\sqrt{370}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{370}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{370}}{10} when ± is plus.

$$x=\frac{\sqrt{370}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{370}}{10} when ± is minus.

$$x=-\frac{\sqrt{370}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{370}}{5} x=-\frac{\sqrt{370}}{5}$$