Solve b^2-169=0

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

Solve for b

$$b=13$$

$$b=-13$$

Steps Using Difference of Squares

Consider b^{2}-169. Rewrite b^{2}-169 as b^{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).

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

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

$$b=13 b=-13$$

Steps by Finding Square Root

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

$$b^{2}=169$$

Take the square root of both sides of the equation.

$$b=13 b=-13$$

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.

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

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}.

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

Square 0.

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

Multiply -4 times -169.

$$b=\frac{0±\sqrt{676}}{2}$$

Take the square root of 676.

$$b=\frac{0±26}{2}$$

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

$$b=13$$

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

$$b=-13$$

The equation is now solved.

$$b=13 b=-13$$