Solve {l}{k/12=3/k=k-3/k}{k/12=frac{3}{k}}

$$\left. \begin{array} { l } { \frac { k } { 12 } = \frac { 3 } { k } = \frac { k - 3 } { k } } \\ { \frac { k } { 12 } = \frac { 3 } { k } } \end{array} \right.$$

Solve for k

$$k=6$$

$$k=-6$$

Steps by Finding Square Root

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12k, the least common multiple of 12,k.

$$kk=12\times 3$$

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

$$k^{2}=12\times 3$$

Multiply 12 and 3 to get 36.

$$k^{2}=36$$

Take the square root of both sides of the equation.

$$k=6 k=-6$$

Steps Using the Quadratic Formula

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12k, the least common multiple of 12,k.

$$kk=12\times 3$$

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

$$k^{2}=12\times 3$$

Multiply 12 and 3 to get 36.

$$k^{2}=36$$

Subtract 36 from both sides.

$$k^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$k=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$k=\frac{0±12}{2}$$

Now solve the equation k=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$k=6$$

Now solve the equation k=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$k=-6$$

The equation is now solved.

$$k=6 k=-6$$