Solve x/25=16/x

$$\frac { x } { 25 } = \frac { 16 } { x }$$

Solve for x

$$x=20$$

$$x=-20$$

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 25x, the least common multiple of 25,x.

$$xx=25\times 16$$

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

$$x^{2}=25\times 16$$

Multiply 25 and 16 to get 400.

$$x^{2}=400$$

Take the square root of both sides of the equation.

$$x=20 x=-20$$

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 25x, the least common multiple of 25,x.

$$xx=25\times 16$$

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

$$x^{2}=25\times 16$$

Multiply 25 and 16 to get 400.

$$x^{2}=400$$

Subtract 400 from both sides.

$$x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-400\right)}}{2}$$

Multiply -4 times -400.

$$x=\frac{0±\sqrt{1600}}{2}$$

Take the square root of 1600.

$$x=\frac{0±40}{2}$$

Now solve the equation x=\frac{0±40}{2} when ± is plus. Divide 40 by 2.

$$x=20$$

Now solve the equation x=\frac{0±40}{2} when ± is minus. Divide -40 by 2.

$$x=-20$$

The equation is now solved.

$$x=20 x=-20$$