Solve x^2-169=0

$${ x }^{ 2 } -169=0$$

Solve for x

$$x=13$$

$$x=-13$$

Steps Using Difference of Squares

Consider x^{2}-169. Rewrite x^{2}-169 as x^{2}-13^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-13\right)\left(x+13\right)=0$$

To find equation solutions, solve x-13=0 and x+13=0.

$$x=13 x=-13$$

Steps by Finding Square Root

Add 169 to both sides. Anything plus zero gives itself.

$$x^{2}=169$$

Take the square root of both sides of the equation.

$$x=13 x=-13$$

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.

$$x^{2}-169=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

Multiply -4 times -169.

$$x=\frac{0±\sqrt{676}}{2}$$

Take the square root of 676.

$$x=\frac{0±26}{2}$$

Now solve the equation x=\frac{0±26}{2} when ± is plus. Divide 26 by 2.

$$x=13$$

Now solve the equation x=\frac{0±26}{2} when ± is minus. Divide -26 by 2.

$$x=-13$$

The equation is now solved.

$$x=13 x=-13$$