Question

Examine the following steps in the solution to 5𝑥2 − 5 = 0

5(𝑥2 − 1) = 0

5(𝑥 − 1)(𝑥 + 1) = 0

𝑥 − 1 = 0

or

𝑥 + 1 = 0

𝑥 = 1

or

𝑥

= −1

What happened to 5? Explain.

Answer 1

$5x^2−5=0$

This is the given equation

$5x^2−5=0\\5(x^2−1)=0\\(x^2−1)=\frac{0}{5}\\x^2−1=0\\(x+1)(x−1)=0\\x=1 \\or\\ x=−1$

5 got divided by 0