Solve 11/x=x/5

$$\frac{ 11 }{ x } = \frac{ x }{ 5 }$$

Solve for x

$$x=\sqrt{55}\approx 7.416198487$$

$$x=-\sqrt{55}\approx -7.416198487$$

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 5x, the least common multiple of x,5.

$$5\times 11=xx$$

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

$$5\times 11=x^{2}$$

Multiply 5 and 11 to get 55.

$$55=x^{2}$$

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

$$x^{2}=55$$

Take the square root of both sides of the equation.

$$x=\sqrt{55} x=-\sqrt{55}$$

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 5x, the least common multiple of x,5.

$$5\times 11=xx$$

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

$$5\times 11=x^{2}$$

Multiply 5 and 11 to get 55.

$$55=x^{2}$$

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

$$x^{2}=55$$

Subtract 55 from both sides.

$$x^{2}-55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-55\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-55\right)}}{2}$$

Multiply -4 times -55.

$$x=\frac{0±\sqrt{220}}{2}$$

Take the square root of 220.

$$x=\frac{0±2\sqrt{55}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{55}}{2} when ± is plus.

$$x=\sqrt{55}$$

Now solve the equation x=\frac{0±2\sqrt{55}}{2} when ± is minus.

$$x=-\sqrt{55}$$

The equation is now solved.

$$x=\sqrt{55} x=-\sqrt{55}$$