In one sentence, describe what the following article is about: Let's say you're working with the following equation: 3x2 - 4x + 5. To factor out a three from the first two terms, simply pull out a 3 and place it around a set of parenthesis around both terms, while dividing each term by 3. 3x2 divided by 3 is simply x2 and 4x divided by 3 is 4/3x. So, the new equation should look like this: 3(x2 - 4/3x) + 5. The 5 will remain outside of the equation because you did not divide it by 3. The second term, also known as the b term in the equation, is 4/3. Halve the second term, or divide it by 2 first. 4/3 2, or 4/3 x 1/2, is equal to 2/3. Now, square this term by squaring both the numerator and denominator of the fraction. (2/3)2 = 4/9. Write this term down. You'll need this "extra" term to turn the first three terms in this equation into a perfect square. But you have to remember that you added it by subtracting it from the equation as well. Though obviously, it won't do you much good to simply combine the terms -- you'll be back where you started. The new equation should look like this: 3( x2 - 4/3 x + 4/9 - 4/9) + 5. Since you're working with a coefficient of 3 outside the parentheses, you can't just pull out the -4/9. You'll have to multiply it by 3 first. -4/9 x 3 = -12/9, or -4/3. If you're not working with an equation with a coefficient other than 1 over the x2 term, then you could skip this step. Right now, you're left with 3(x2 -4/3x +4/9) within the parentheses. You worked backwards to get the 4/9, which was really another way of finding the term that would complete the square. So, you can rewrite those terms like this: 3(x - 2/3)2. All you had to do was halve the second term and remove the third. You can check that this works by multiplying it out to see that it gives you the first three terms of the equation. 3(x - 2/3)2 = 3(x - 2/3)(x -2/3) = 3[(x2 -2/3x -2/3x + 4/9)] 3(x2 - 4/3x + 4/9) You're left with two constant terms, or terms that aren't attached to a variable. Right now, you're left with 3(x - 2/3)2 - 4/3 + 5. All you have to do is add up -4/3 and 5 to get 11/3. You do this by setting them to the same denominator: -4/3 and 15/3, and then adding the numerators to get 11, and keeping the denominator as 3. -4/3 + 15/3 = 11/3. You're all done. The final equation is 3(x - 2/3)2 + 11/3. You can remove the coefficient of 3 by dividing both parts of the equation to get (x - 2/3)2 + 11/9. You have now successfully placed the equation into vertex form, which is a( x - h )2 + k, where k represents the constant term.
Summary: Write down the equation. Factor out the coefficient of the squared term from the first 2 terms. Halve the second term and square it. Add and subtract this term from the equation. Pull the term you subtracted out of the parenthesis. Convert the terms in the parentheses into a perfect square. Combine the constant terms. Write the equation in vertex form.

Problem: Article: Some adhesives, such as "cut-back" adhesives and "mastic," were often mixed with asbestos up until the late 1980s, and are still occasionally used today. These adhesives were most commonly used to bond the floor to tiles or to heating and air ducts, not to carpets, and are often black in color. If you suspect your adhesive contains asbestos, do not use this method, as sanding or scraping the dry adhesive can release dangerous asbestos fibers into the air. Refer to the solvent section instead, or hire a professional to remove the asbestos. Chipping and scraping off the old adhesive can be tedious, although not much more so than using a solvent. The main benefit is a lower risk of discoloring the wood or clogging its pores. After using this method, it should be easy to bond a new stain or finish to the wood. However, if there is an existing finish you plan to leave on, or if you plan to cover the floor with a new carpet, the solvent method may save you some time. Note: renting a wet/dry vacuum from a tool rental service is highly recommended for quick, safe cleanup after the adhesive is removed. If you're lucky, the adhesive will chip right off when you apply pressure with a putty knife. Some areas may take more pressure than others. Only use a plastic putty knife, not metal, to avoid scratching the floor. If the adhesive only comes off in tiny chips, try making it easier to remove with dry ice as described below, or use solvents instead. Pick the widest putty knife you can find to make the task less tedious. If you plan to apply a new stain or finish to the floor, this is your best option for making adhesive removal easier without affecting the wood pores. Place pieces of dry ice in a cookie tray and slide the tray over each section of adhesive before you chip, to make the glue brittle and easier to remove. Always follow these safety precautions before you buy dry ice: Wear thick gloves while handling dry ice, as the extreme cold can instantly cause painful skin damage. Always store and work with dry ice in a well-ventilated room, and leave immediately if you have trouble breathing. Dry ice is solid carbon dioxide, and can fill a small space with unbreathable gas. Do not store in an airtight container, which may explode as the dry ice expands into gas. Clean up the chips of adhesive using a wet/dry vacuum if possible, or a broom. Your local government may require you to dispose of them at a waste collection center, rather than adding it to your ordinary trash, since some adhesives contain toxic materials. However, since you did not use any solvents, you may be able to dispose of adhesives normally; contact local waste collection services to find out about local regulations. The floor may need to be sanded to clear up any scuff marks caused by the carpet installation or the glue removal. Use 16 or 24 grit sandpaper, but go slowly to avoid scraping into the wood. Optionally, sand away the old finish in preparation for adding a new stain and/or finish. Sanding away the adhesive itself is not recommended, as the sandpaper will quickly get clogged and need replacing. Heat from the friction may also melt the adhesive, which can be messy.
Summary:
Do not use this method on adhesives containing asbestos. Know the benefits of this method. Use a plastic putty knife to chip off the adhesive. Consider using dry ice. Dispose of the old glue. Sand the floor down (optional).