Solve 25/x=x/27

$$\frac { 25 } { x } = \frac { x } { 27 }$$

Solve for x

$$x=15\sqrt{3}\approx 25.980762114$$

$$x=-15\sqrt{3}\approx -25.980762114$$

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 27x, the least common multiple of x,27.

$$27\times 25=xx$$

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

$$27\times 25=x^{2}$$

Multiply 27 and 25 to get 675.

$$675=x^{2}$$

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

$$x^{2}=675$$

Take the square root of both sides of the equation.

$$x=15\sqrt{3} x=-15\sqrt{3}$$

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 27x, the least common multiple of x,27.

$$27\times 25=xx$$

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

$$27\times 25=x^{2}$$

Multiply 27 and 25 to get 675.

$$675=x^{2}$$

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

$$x^{2}=675$$

Subtract 675 from both sides.

$$x^{2}-675=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -675 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-675\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-675\right)}}{2}$$

Multiply -4 times -675.

$$x=\frac{0±\sqrt{2700}}{2}$$

Take the square root of 2700.

$$x=\frac{0±30\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±30\sqrt{3}}{2} when ± is plus.

$$x=15\sqrt{3}$$

Now solve the equation x=\frac{0±30\sqrt{3}}{2} when ± is minus.

$$x=-15\sqrt{3}$$

The equation is now solved.

$$x=15\sqrt{3} x=-15\sqrt{3}$$