Algebra - Quadratic Equations

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Section 2.5 : Quadratic Equations - Part I

15. Use the Square Root Property to solve the equation.

\[{\left( {z - 2} \right)^2} - 36 = 0\]

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There 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 2

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