Solve the equation 5x^2 - 20 = 0.

Step-by-step solution

1. 1

   Notice there is no linear term. The equation has the form $ax^2+c=0$ with $b=0$. That means the square-root method applies directly and the two roots will be negatives of each other.

2. 2

   Isolate the square term. Add $20$, then divide by $5$:

   $5x^2=20\quad\Longrightarrow\quad x^2=4$

3. 3

   Take the square root of both sides, keeping both signs. The equation $x^2=4$ asks which numbers square to $4$, and there are two:

   $x=\pm\sqrt{4}=\pm 2$

   Writing only $x=2$ is the classic omission: $\sqrt{4}$ denotes the principal (non-negative) root, so the $\pm$ has to be supplied by hand.

4. 4

   Cross-check by factoring. The same answer falls out of the difference of squares:

   $5x^2-20=5(x^2-4)=5(x-2)(x+2)$

   which is zero exactly when $x=2$ or $x=-2$ $\checkmark$. Substituting: $5(4)-20=0$ for both values.