Solve 2-1=16^2/b^2

$$2 - 1 = \frac { 16 ^ { 2 } } { b ^ { 2 } }$$

Solve for b

$$b=16$$

$$b=-16$$

Steps Using Difference of Squares

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}.

$$b^{2}\times 2+b^{2}\left(-1\right)=16^{2}$$

Combine b^{2}\times 2 and b^{2}\left(-1\right) to get b^{2}.

$$b^{2}=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$b^{2}=256$$

Subtract 256 from both sides.

$$b^{2}-256=0$$

Consider b^{2}-256. Rewrite b^{2}-256 as b^{2}-16^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(b-16\right)\left(b+16\right)=0$$

To find equation solutions, solve b-16=0 and b+16=0.

$$b=16 b=-16$$

Steps by Finding Square Root

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}.

$$b^{2}\times 2+b^{2}\left(-1\right)=16^{2}$$

Combine b^{2}\times 2 and b^{2}\left(-1\right) to get b^{2}.

$$b^{2}=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$b^{2}=256$$

Take the square root of both sides of the equation.

$$b=16 b=-16$$

Steps Using the Quadratic Formula

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}.

$$b^{2}\times 2+b^{2}\left(-1\right)=16^{2}$$

Combine b^{2}\times 2 and b^{2}\left(-1\right) to get b^{2}.

$$b^{2}=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$b^{2}=256$$

Subtract 256 from both sides.

$$b^{2}-256=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -256 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-256\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-256\right)}}{2}$$

Multiply -4 times -256.

$$b=\frac{0±\sqrt{1024}}{2}$$

Take the square root of 1024.

$$b=\frac{0±32}{2}$$

Now solve the equation b=\frac{0±32}{2} when ± is plus. Divide 32 by 2.

$$b=16$$

Now solve the equation b=\frac{0±32}{2} when ± is minus. Divide -32 by 2.

$$b=-16$$

The equation is now solved.

$$b=16 b=-16$$