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Expert: Sherry Wallin - 2/23/2009


Question
2x-7x-15=0
how to solve step by step

Answer

complete the square
Hi Ashaunti~
    There are several methods to completing the square but since you are asking I am going to assume you've never done it before and give you the version that I find is the simplest for my students, if fact I will attached a couple of worksheets with sample problems worked out that I typically give to my students when I cover it. I also will give you a link to a utube video where the instructor covers it nicely...

http://www.veoh.com/videos/v1227303eF3Gpz9q

You want your quadratic equation to look like ax^2+bx = c where a = 1
so in your case we need to divide all terms by 2 to make the 2 a 1.

(2x^2)/2-7x/2-15/2 = 0 and move the -15/2 to the right side
x^2 -(7/2)x        = +15/2

The next step is to take 1/2 the coefficient on x which in your case the coefficient on x is -7/2 so 1/2 * -7/2 = -7/4

We want to add this to both sides of the equation, on the left we will leave it as a number squared but on the right we will simplify it
(-7/2)^2 = (-7/2)(-7/2) = 49/4

so we have:
x^2 -(7/2)x +(-7/2)^2 = 49/4+15/2 simplify on the right gives us
49/4+15/2 = 49/4+30/4 = 79/4, so now we have:
x^2 -(7/2)x +(-7/2)^2 = 79/4, on the left we have created a perfect square, the form of a perfect square is such that it can be written as
(a+b)^2 or (a-b)^2
(x-7/2)^2 = 79/2 but we need to get x by itself so we take the square root of both sides getting:
sqrt(x-7/2)^2 = +-sqrt(79/4) which simplifies to +-sqrt(79)/2 on the right and on the left we have x-(7/2), thus

x-(7/2) =+- sqrt(79)/2 gives us x = 7/2 +-sqrt(79)/2 so it must be that x = 7/2 +sqrt(79)/2 or x = 7/2 -sqrt(79)/2.

I hope this helps you.

Math Prof

Make sure you look at the materials I attached as images, you can open them in paint or some place you know you can open images. The video link is done very well although the guy is sort of boring in his presentation

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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