Solve p^2=169

$$p ^ { 2 } = 169$$

Solve for p

$$p=13$$

$$p=-13$$

Steps Using Difference of Squares

Subtract 169 from both sides.

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

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

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

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

$$p=13 p=-13$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$p=13 p=-13$$

Steps Using the Quadratic Formula

Subtract 169 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -169.

$$p=\frac{0±\sqrt{676}}{2}$$

Take the square root of 676.

$$p=\frac{0±26}{2}$$

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

$$p=13$$

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

$$p=-13$$

The equation is now solved.

$$p=13 p=-13$$