Solving Quadratic Equations with Square Roots

Before we will try to solve the given equation, let's recall the number of real solutions to a quadratic equation $x^2=d,$ depending on the sign of $d.$

• When $d>0,$ $x^2=d$ has two real solutions, $x=\pm \sqrt{d}.$
• When $d=0,$ $x^2=d$ has one real solution, $x=0.$
• When $d<0,$ $x^2=d$ has no real solution.

Notice that in our case $d=169,$ which is positive, so there are two real solutions to the given equation. To find them by taking the square roots, we need to consider the positive and negative solutions. We found that $x=\pm 13.$ Thus, there are two solutions for the equation: $x=13$ and $x=\text{-}13.$