Some quadratic equations can be solved by performing the same operation on each side of the equal sign and reasoning about which values for the variable would make the equation true.

Suppose we wanted to solve $3(x+1)^2-75=0$. We can proceed like this:

• If $x+1 = 5$, then $x=4$.
• If $x+1 = \text-5$, then $x=\text-6$.

This means that both $x=4$ and $x=\text-6$ make the equation true and are solutions to the equation.

Many quadratic equations have 2 solutions, but some have only 1 or no solution.