Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 2.5 : Quadratic Equations - Part I
15. Use the Square Root Property to solve the equation.
\[{\left( {z - 2} \right)^2} - 36 = 0\]Show All Steps Hide All Steps
Start SolutionThere really isn’t too much to this problem. Just recall that we need to get the squared term on one side of the equation by itself with a coefficient of one. For this problem that gives,
\[{\left( {z - 2} \right)^2} = 36\] Show Step 2Using the Square Root Property gives,
\[z - 2 = \pm \sqrt {36} = \pm 6\]To finish this off all we need to do then is solve for \(z\) by adding 2 to both sides. This gives,
\[z = 2 \pm 6\hspace{0.25in} \Rightarrow \hspace{0.25in}z = 2 - 6 = - 4,\,\,\,\,\,\,z = 2 + 6 = 8\]So, after we did a little arithmetic, have the following two solutions : \(\require{bbox} \bbox[2pt,border:1px solid black]{{z = - 4\,\,\,{\mbox{and }}z = 8}}\).