Question

Part 1: solve the following using one of the methods listed below. Show all work Part 2: using complete sentences,explain why you chose the method you used 2(points) Equation : 0=x^2+10x+5. Methods: completing the square,factoring,quadratic formula,graphing

Answer 1

Hi, Dreamer,

I jumped in and solved the given polynomial for x in two different ways: completing the square and quadratic formula. I eliminated use of the method of factoring (if you want to know why, please ask), and did not try graphing because of its inexactness (we'd have to estimate the values of the roots/solutions visually, which is hard when the solutions/roots are nonrational).

Have you solved quadratic equations before using "completing the square"? I need to know this to know how much to explain (or to assume you already know).

Here are some of the steps involved in completing the square:

\[x ^{2} +10x+5=0\]

\[x ^{2} +10x+25-25+5=0\]

\[\left( x+5 \right)^{2}-20=0\]

\[\left( x+5 \right)^{2}=20\]

\[x+5=\sqrt{20}or -\sqrt{20}\]
\[x=-5+\sqrt{20}\]
or
\[x=-5-\sqrt{20}\]
Note that \[\sqrt{20}\] can be reduced.

The solution using the quadratic formula is roughly as easy to do.

Hope this info enables you to answer both parts of your question.