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For more information, please see full course syllabus of Algebra 2
For more information, please see full course syllabus of Algebra 2
Algebra 2 Completing the Square
Lecture Description
You can solve quadratic equations by taking the square root of both sides of the equation. To do this, the quadratic expression must be a perfect square, which is not always the case. To get a perfect square, we use the method called completing the square. The principle of completing the square is to take one-half of the coefficient of the linear term, square it, and add it to both sides of the equation. However, if the coefficient of the quadratic term is not 1, we need to do some additional work, which you'll see in this lecture. Note that the solutions to a quadratic equation may be both real and complex numbers.
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Last reply by: Dr Carleen Eaton
Wed Nov 6, 2013 12:48 AM
Post by Chateau Siqueira on September 27, 2013
Thank you for your lectures Dr. Eaton. My college algebra class is vary fast paced which sometimes I do not absorb all the material but then I come over here an it all makes sense! I appreciate your time.
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Post by julius mogyorossy on September 1, 2013
It seems to me that one of your solutions may not be a negative #, that is what I thought at first, that your solutions may not even be the same number, one positive, one negative, a simple example, (x-2)'2=4, it is easy hear to see what the solutions are, 4 and 0. If you worked out this problem it would be, x=2+-^4, the square root of 4 is 2 so that would be 2+2=4, 2-2=0, x=4, and x=0. But don't take my word on it, ask Dr. Carleen. (x-2)'2=4 is a question, asking you what two values for x in that equation =4.
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Post by julius mogyorossy on September 1, 2013
I meant to say (x-4)'2=5 reminds me of absolute value equations. I really understand what this is saying now, x=4+-^5 is just another way to say the same thing.
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Post by julius mogyorossy on September 1, 2013
The (x-4)'2=5 reminds me of inequalities.
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Last reply by: Dr Carleen Eaton
Tue Jun 4, 2013 8:10 PM
Post by Kavita Agrawal on June 3, 2013
At about 6 min., you said that -8^2 = 64. -8^2, however, equals -64 (because of the order of operations, and exponents come before multiplying.) I think that part would make more sense if it had parentheses around it.
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Post by julius mogyorossy on March 25, 2012
It seems that if you can divide, b, in to two equal parts, getting whole numbers, you then just multiply those two equal parts times each other to get the constant in the perfect square trinomial, the first operator can be positive or negative, the second one in the perfect square trinomial will always be positive, is this correct.
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Post by Ken Mullin on January 27, 2012
Nice review of completing thr square...
Espcially like the emphasis on ISOLATING (b^2)/4 and adding result to both sides.
Some textbooks use the reciprocal of 2 and so makes the operation seem more difficult than it otherwise is...