Solve 1/2=16/z^2-4

$$\frac { 1 } { 2 } = \frac { 16 } { z ^ { 2 } - 4 }$$

Solve for z

$$z=6$$

$$z=-6$$

Steps Using Difference of Squares

Variable z cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 2\left(z-2\right)\left(z+2\right), the least common multiple of 2,z^{2}-4.

$$\left(z-2\right)\left(z+2\right)=2\times 16$$

Consider \left(z-2\right)\left(z+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$z^{2}-4=2\times 16$$

Multiply 2 and 16 to get 32.

$$z^{2}-4=32$$

Subtract 32 from both sides.

$$z^{2}-4-32=0$$

Subtract 32 from -4 to get -36.

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

Consider z^{2}-36. Rewrite z^{2}-36 as z^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-6\right)\left(z+6\right)=0$$

To find equation solutions, solve z-6=0 and z+6=0.

$$z=6 z=-6$$

Steps by Finding Square Root

Variable z cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 2\left(z-2\right)\left(z+2\right), the least common multiple of 2,z^{2}-4.

$$\left(z-2\right)\left(z+2\right)=2\times 16$$

Consider \left(z-2\right)\left(z+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$z^{2}-4=2\times 16$$

Multiply 2 and 16 to get 32.

$$z^{2}-4=32$$

Add 4 to both sides.

$$z^{2}=32+4$$

Add 32 and 4 to get 36.

$$z^{2}=36$$

Take the square root of both sides of the equation.

$$z=6 z=-6$$

Steps Using the Quadratic Formula

Variable z cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 2\left(z-2\right)\left(z+2\right), the least common multiple of 2,z^{2}-4.

$$\left(z-2\right)\left(z+2\right)=2\times 16$$

Consider \left(z-2\right)\left(z+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$z^{2}-4=2\times 16$$

Multiply 2 and 16 to get 32.

$$z^{2}-4=32$$

Subtract 32 from both sides.

$$z^{2}-4-32=0$$

Subtract 32 from -4 to get -36.

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

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}.

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

Square 0.

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

Multiply -4 times -36.

$$z=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$z=\frac{0±12}{2}$$

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

$$z=6$$

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

$$z=-6$$

The equation is now solved.

$$z=6 z=-6$$