Solve x/64=39/x

$$\frac { x } { 64 } = \frac { 39 } { x }$$

Solve for x

$$x=8\sqrt{39}\approx 49.959983987$$

$$x=-8\sqrt{39}\approx -49.959983987$$

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 64x, the least common multiple of 64,x.

$$xx=64\times 39$$

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

$$x^{2}=64\times 39$$

Multiply 64 and 39 to get 2496.

$$x^{2}=2496$$

Take the square root of both sides of the equation.

$$x=8\sqrt{39} x=-8\sqrt{39}$$

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 64x, the least common multiple of 64,x.

$$xx=64\times 39$$

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

$$x^{2}=64\times 39$$

Multiply 64 and 39 to get 2496.

$$x^{2}=2496$$

Subtract 2496 from both sides.

$$x^{2}-2496=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2496 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2496\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2496\right)}}{2}$$

Multiply -4 times -2496.

$$x=\frac{0±\sqrt{9984}}{2}$$

Take the square root of 9984.

$$x=\frac{0±16\sqrt{39}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{39}}{2} when ± is plus.

$$x=8\sqrt{39}$$

Now solve the equation x=\frac{0±16\sqrt{39}}{2} when ± is minus.

$$x=-8\sqrt{39}$$

The equation is now solved.

$$x=8\sqrt{39} x=-8\sqrt{39}$$