Solve 1/b^2=1

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

Solve for b

$$b=1$$

$$b=-1$$

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}.

$$1=b^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}=1$$

Subtract 1 from both sides.

$$b^{2}-1=0$$

Consider b^{2}-1. Rewrite b^{2}-1 as b^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(b-1\right)\left(b+1\right)=0$$

To find equation solutions, solve b-1=0 and b+1=0.

$$b=1 b=-1$$

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}.

$$1=b^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}=1$$

Take the square root of both sides of the equation.

$$b=1 b=-1$$

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}.

$$1=b^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}=1$$

Subtract 1 from both sides.

$$b^{2}-1=0$$

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

$$b=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

Multiply -4 times -1.

$$b=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$b=\frac{0±2}{2}$$

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

$$b=1$$

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

$$b=-1$$

The equation is now solved.

$$b=1 b=-1$$