Problem: Article: Smiling is never overrated. Though you may think that smiling won’t have an impact on what people think of you, taking the time to smile at people will show them that you’re happy to be in their presence and that you’re a warm, friendly person who is worth talking to. Whether you’re talking to people or just walking by them, make the effort to smile, the next time around. Besides, scientific research has shown that smiling actually makes you feel happier, so everybody wins! Make an effort to smile at at least 10 people today. Once you get into the habit of it, it’ll feel perfectly natural. If you make it clear that you’re fully engaged in the conversation and have nowhere else you’d rather be, then people will be much more likely to be drawn to you. Don’t check your phone every five minutes, look around the room, play with your nails, or talk about the meeting you have to go to later, or people will feel like chopped liver when you talk to them. Instead, take the time to make eye contact, ask people questions, and make them feel like you’re enjoying the moment you’re spending talking to them.  It can be hard to shut off those distractions and to learn to live in the now. Sometimes the first step is unplugging. If you’re talking to a co-worker, step away from your computer. If you have a dinner date with a close friend, turn your phone off for a few hours. Give the person you’re speaking to the attention he or she deserves. Take the time to read his or her body language and facial expressions to see how he or she is feeling, instead of seeing what all the other people in the room are up to. Another easy way to make people like you is to have a positive demeanor. If you radiate positive energy instead of complaining, making fun of people, or just being mean, then people will be more drawn to you because they’ll feel energized in your presence. Work on focusing on the good things in life and learning to laugh at the bad. If you want to get along with people, then it’ll be much easier if you approach life with a smile instead of a frown.  Every time you hear yourself making a negative comment, make two or three positive comments to compensate. It’s okay to be negative every once in a while, but you should focus on the good things ahead instead of the ones that are dragging you down. Another way to keep things positive is to work on complimenting people more often. This sets a more positive tone to the conversation and may lead to some compliments in return. Another way to cultivate positivity is to surround yourself with positive people. Their mindset and behavior will be contagious and will help you get along with others. Bringing around a fun, positive friend can also help you get along with people, too. If you want to make a good impression on people, then you have to learn how to read them quickly to understand what kind of a person you’re dealing with. If you see that you’re facing a conservative from the South, then the subjects you discuss may be quite different than they would be if you were talking to a hippie from Berkeley; make sure you consider the person you’re talking to before you introduce what might be a controversial subject. If you want to get along with people, then it’s important to know what they would and would not want to hear so you can make a positive first impression.  Watch how the other person responds to others to get a better sense of things kinds of things that will or will not appeal to him. If the person cracks up at the raunchy joke of another person, then you’ll know that that kind of humor is okay. Be aware of the age of the person, too. An older person may not appreciate a comment about how old you’re getting when you’re a decade younger; a younger person may not understand one of your cultural references. Education level can play a part in this, too. If you’re talking to a person with a PhD in English, then he may be insulted if you try to explain who Ernest Hemingway is. Another skill that people who make good first impressions posses is knowing how to make small talk. Though you may think it’s frivolous, small talk is what leads you to have deeper conversations and to really connect with people, so it’s important to know how to chat with new people when you first meet them. All you have to do is ask lighthearted questions to get to know them a bit, learn to banter, and be comfortable feeling out the personality of a new person. Here are some tips for how to make small talk effectively:  Compliment an item that the person is using or wearing. It may lead to a good conversation. Don’t be wary of discussing the weather. It could lead to a conversation about your weekend plans or even your hobbies. Ask questions that require more of a response than a “yes” or “no” answer. This can help get the conversation going. Don’t put too much pressure on an awkward silence. Instead of commenting on it, ask a simple question or make a statement to move the conversation forward. One of the easiest ways to make a good first impression is to show a genuine interest in them as soon as you shake their hands. You don’t have to ask them a million questions, but show an interest in their ideas, their hobbies, or their background without being too nosy. The truth is, people love it when others show an interest in them, and acting like you’d rather get to know them instead of talking about yourself can go a long way in helping you get along with others.  The best way to show a genuine interest is to really listen instead of going through the motions until it’s your turn to speak. When a person gives good news, make sure he sees that you really care instead of just glossing it over. If a person is an expert at something, ask him questions about it to show that you’re interested in what he has to say.
Summary: Smile. Be fully present. Cultivate positivity. Know your audience. Make small talk. Show a genuine interest in people.

Problem: Article: After you have eliminated all the radicals from the problem, move all the terms to one side of the equation and combine like terms. Returning to the working sample problem, this looks as follows:  x−1=x2−14x+49{\displaystyle x-1=x^{2}-14x+49} 0=x2−15x+50{\displaystyle 0=x^{2}-15x+50} In most cases, this step will create a quadratic polynomial. This is an equation that contains an x2{\displaystyle x^{2}} term as its highest variable. If the original radical was something other than a square root (such as a cube root or fourth root, for example), then you may have a more difficult problem. We will focus on the quadratic for this article. You may be able to solve the quadratic equation by factoring, or you can go directly to the quadratic formula. In this case, the sample problem, 0=x2−15x+50{\displaystyle 0=x^{2}-15x+50}, can be factored into the two binomial factors of (x−5){\displaystyle (x-5)} and (x−10){\displaystyle (x-10)}. Factoring the quadratic equation in this case suggests two possible solutions. Because the quadratic equation is equal to 0, you find the solutions by setting each factor equal to 0 and then solve.  In the working problem, the two factors are (x−5){\displaystyle (x-5)} and (x−10){\displaystyle (x-10)}. Set each of these equal to 0 to get the solutions x=5{\displaystyle x=5} and x=10{\displaystyle x=10}. With another problem, you may not be able to factor and would then have to use the quadratic formula to find the solution.
Summary:
Consolidate and combine like terms. Solve the equation. Determine your solutions.