Solve f_x^2=1

$$f _ { x } ^ { 2 } = 1$$

Solve for f_x

$$f_{x}=1$$

$$f_{x}=-1$$

Steps Using Difference of Squares

Subtract 1 from both sides.

$$f_{x}^{2}-1=0$$

Consider f_{x}^{2}-1. Rewrite f_{x}^{2}-1 as f_{x}^{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).

$$\left(f_{x}-1\right)\left(f_{x}+1\right)=0$$

To find equation solutions, solve f_{x}-1=0 and f_{x}+1=0.

$$f_{x}=1 f_{x}=-1$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$f_{x}=1 f_{x}=-1$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$f_{x}^{2}-1=0$$

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}.

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

Square 0.

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

Multiply -4 times -1.

$$f_{x}=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$f_{x}=\frac{0±2}{2}$$

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

$$f_{x}=1$$

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

$$f_{x}=-1$$

The equation is now solved.

$$f_{x}=1 f_{x}=-1$$