Question

WILL GIVE BRAINLIEST, THANKS, AND 5 STARS! PLEASE HELP ME!

Answer 1

Answer:

-4 and 4

Step-by-step explanation:

Method 1

Apply Difference of Two Squares Formula: $a^2-b^2=(a+b)(a-b)$

Given  $x^2-16=0$

Rewrite 16 as 4²

Therefore, $a^2=x^2$ and $b^2=4^2$

$\implies a = \sqrt{x^2}=x$

$\implies b=\sqrt{4^2} =4$

$\implies x^2-16^2=(x+4)(x-4)$

$\implies (x+4)(x-4)=0$

$\implies (x+4)=0 \implies x=-4$

$\implies (x-4)=0 \implies x=4$

Method 2

Given equation:

$x^2-16=0$

Add 16 to both sides:

$\implies x^2-16+16=0 + 16$

$\implies x^2=16$

Square root both sides:

$\implies \sqrt{x^2}=\sqrt{16}$

$\implies x=\pm4$

Therefore, x = -4, x = 4