In one sentence, describe what the following article is about: Recall that after isolating the radical on one side of the equation, you then squared both sides to remove the radical sign. This is a necessary step to solving the problem. However, the squaring operation is what creates the extraneous solutions. Remember some basic mathematics, that both a negative and a positive number, when squared, will give the same result. For example, (−3)2{\displaystyle (-3)^{2}} and 32{\displaystyle 3^{2}} both give the answer of 9{\displaystyle 9}. However, both the negative and positive numbers might not be solutions to whatever problem you are solving. The one that does not work is called the extraneous solution. After you have found the solutions to your problem, you may have found one, two or more different possible values for the variable. You need to check each of these in the original problem to see which work. Remember that the original problem here was x−1+4=x−3{\displaystyle {\sqrt {x-1}}+4=x-3}.  First check the solution x=5{\displaystyle x=5}:  x−1+4=x−3{\displaystyle {\sqrt {x-1}}+4=x-3}  5−1+4=5−3{\displaystyle {\sqrt {5-1}}+4=5-3} ………. (substitute 5 for x) 4+4=5−3{\displaystyle {\sqrt {4}}+4=5-3} 2+4=5−3{\displaystyle 2+4=5-3}  6=2{\displaystyle 6=2}. Because your result is an incorrect statement, the original solution of x=5{\displaystyle x=5} must be an extraneous solution that was caused by the squaring process.   Check the second solution x=10{\displaystyle x=10}:  x−1+4=x−3{\displaystyle {\sqrt {x-1}}+4=x-3} 10−1+4=10−3{\displaystyle {\sqrt {10-1}}+4=10-3} 9+4=10−3{\displaystyle {\sqrt {9}}+4=10-3} 3+4=10−3{\displaystyle 3+4=10-3} 7=7{\displaystyle 7=7} In this case, you get a true statement. This shows that the solution x=10{\displaystyle x=10} is a true solution to the original problem. The extraneous solution is incorrect and can be discarded. Whatever remains is the answer to your problem. In this case, you would report that x=10{\displaystyle x=10}.
Summary: Recognize the potential for an extraneous solution. Test each of your solutions in the original problem. Discard the extraneous solution and report your result.

In one sentence, describe what the following article is about: You should treat finding a new job like a job in itself. Budget several hours each day, at a set time, to search for jobs. For example, you might decide that you will spend one hour each day at 1 p.m. making a list of five jobs that you're interested in. Then, from 2 p.m. to 5 p.m. you will fill out applications for those five jobs. Take some time to improve your resume and tailor it to the jobs you're interested in. If you're planning to change your line of work, edit your previous employment to emphasize skills that will be relevant to the new line of work. For example, if you were a computer programmer in your previous job and you're hoping to get into investment banking, emphasize the analytical skills required in your previous jobs. Depending on your financial situation, you may need to accept jobs that aren't your dream job. At the beginning of your job search, it's OK to apply only for jobs that you really want. If a few months go by and you're still unemployed, you should consider taking a job that isn't exactly what you're looking for.  For example, if you're searching for a job in programming but you're getting no offers, consider applying for jobs in IT instead. Remember that a non-ideal job doesn't have to be permanent and it may end up leading to other opportunities. Employers will want to know why you're experiencing a period of unemployment. Get in front of the issue by listing it on your resume and having an honest story to tell during interviews.  For example, on your resume you might write, “Laid off due to budget cut-backs. Seeking employment daily for the last two months.” In an interview, explain to your potential employer what you've been doing with your free time. Emphasize any activities that might be selling points. For example, you might say, “I usually apply to five-to-ten jobs a week. In my spare time, I've been learning how to program in HTML.” If you want to develop new skills, unemployment is a good time to consider going back to school. Think about what kind of jobs you want and choose a program that will give you the skills you need to get hired.  Avoid going back to school just to fill time. If you go back to school without a goal in mind, you may just end up accumulating more debt. You can also look for certificate programs or specialized training conferences that are shorter-term and will help hone your skills and make you an attractive candidate. Schooling is an additional expense, but there are many resources available to help fund your education. If you have a low income you may qualify for federal grants that you don't have to repay. If you don't qualify, you may be able to get low-interest loans through the federal government. Fill out the  FAFSA application to find out what aid you qualify for.
Summary: Make a plan. Update your  resume. Be flexible. Make a  good impression on employers. Learn  new skills.

In one sentence, describe what the following article is about: Using the correct lighting can make or break the atmosphere that you want in your secret place.  Try to choose a spot near a window. Natural light will fill your secret space no matter the size of the window or space. If there is no way to put your space near a window, use a small lamp or nightlight to brighten the dark space. Hang a flashlight if there isn’t natural light or an outlet in your secret space. You should always enjoy your secret space and the way to do this is to create the perfect atmosphere. It should be filled with some of your favorite things and scream personality.  Decorations are a great way to express yourself in the space. Use posters, pictures, or anything else you wish to liven up your secret space.  Wallpaper is a great way to add character to your space.   Lay a small rug down in your space to add some color and comfort. Add scent your space with aromatherapy. Make the space smell the way you want. You can do this with air fresheners, flowers, or essential oils. Choosing the right scents define the feeling of your secret space. Include seating in your secret space. Chairs can be comfortable, but they may be too big. Try using pillows or bean bags if you need something smaller. Maybe you’re looking for a spot to sit and think, place to store your favorite pictures, or space to lay down and read a book. With your needs in mind, add some final touches to your secret space.  Fill your secret spot with things to keep you occupied while you’re there. Maybe you want magazines or crafts to fill your time. Think about what you want and be sure to stock up.   If you prefer to store items in your secret space, use hangers, hooks, or storage boxes. You could even stack CDs or books to create a small but neat storage area. If you’re trying to store a lot of things, baskets and closet organizers are a great way to store tons of small items.   Keep drinks or food in your secret spot if you plan to be there for a few hours. Make it as comfortable as possible for yourself.
Summary:
Find the right light. Create an atmosphere. Match your needs.