Solving Quadratic Equations with Square Roots

First we want to isolate the $x^2$-term. After that we can square root both sides of the equation.

The equation then has two real solutions: $x=9$ and $x=\text{-}9.$

Our $x^2$-term stands alone on the left side, so in order to solve the equation we take the square root of both sides. But we cannot calculate the square root of $\text{-}121.$ That is because there is no real number whose square is negative. Therefore, the equation has no real solutions.

After we have isolated the $x^2$-term we can write the equation as $$x^2=\text{-}1.$$ Just like in Part B, this is an equation that lacks real solutions, because we must take the square root of a negative number to solve it.

Let's isolate the $x^2$-term on one side. After that we can square root both sides.