Weekly Math Problem! #37

Completing the Square. One thing that can be super annoying--more than solving a problem--is being told how to solve a problem. 😒 Wait a minute. What happened to my mathematical freedom to choose? 😩 It seems like this is done when the instructor has something up his/her sleeve. You may even feel like you are being tricked on purpose. (Sometimes you are.) However, some instructors do that to see if you've payed attention, while some want to see if you have the ability to transfer prior skills to current topics. Even though many instructors have your best learning interests at heart, it is still annoying. 🙄

This week's WMP! is a very good example of the above. To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to solve a quadratic equation
        ✔️     Completing the square method

WMP! #37 says:

Happy solving!

Check back on Friday, February 12th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Jumping right in, the first thing that needs to be done is to get the quadratic equation in a form that accommodates the completing the square method to commence--a leading coefficient of 1 and the resulting constant isolated:

Now that the quadratic equation is in the proper form, we can go ahead and employ the completing the square method. (Right now it's incomplete. 🤪) This is where some students get tripped up. Notice that the b-term is not an integer but a fraction. It can be annoying to complete the square when the b-term is a fraction, it can be done. Multiply the fraction by 1/2, then square the result.

So, 4/25 is the number that will allow us to complete the square. Here is how to complete the rest of problem, which involves using the square root method to finish solving for x:

 

Remember, there are two solutions that will satisfy the original quadratic equation we were asked to solve. Lastly, we'll separate the plus-minus and round each solution to the nearest ten-thousandths.

Of course there is a graph. 😁

**This plot was created using Geogebra's Graphing Gaclulator.

▪️ How did you find this week's problem?

▪️ Leave your response down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

WMP! #38 here we come!

Cheers!

The Younge Lady