Solve X^2-1=0

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

Solve for X

$$X=1$$

$$X=-1$$

Steps Using Difference of Squares

Consider X^{2}-1. Rewrite X^{2}-1 as 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).

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

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

$$X=1 X=-1$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

$$X^{2}=1$$

Take the square root of both sides of the equation.

$$X=1 X=-1$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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}.

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

Square 0.

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

Multiply -4 times -1.

$$X=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$X=\frac{0±2}{2}$$

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

$$X=1$$

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

$$X=-1$$

The equation is now solved.

$$X=1 X=-1$$