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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 : \(\require{bbox} \bbox[2pt,border:1px solid black]{{z = - 4\,\,\,{\mbox{and }}z = 8}}\).