Solve p^2-64=0

$$p ^ { 2 } - 64 = 0$$

Solve for p

$$p=8$$

$$p=-8$$

Steps Using Difference of Squares

Consider p^{2}-64. Rewrite p^{2}-64 as p^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(p-8\right)\left(p+8\right)=0$$

To find equation solutions, solve p-8=0 and p+8=0.

$$p=8 p=-8$$

Steps by Finding Square Root

Add 64 to both sides. Anything plus zero gives itself.

$$p^{2}=64$$

Take the square root of both sides of the equation.

$$p=8 p=-8$$

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.

$$p^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$p=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$p=\frac{0±16}{2}$$

Now solve the equation p=\frac{0±16}{2} when ± is plus. Divide 16 by 2.

$$p=8$$

Now solve the equation p=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$p=-8$$

The equation is now solved.

$$p=8 p=-8$$