math wiz''s--need algebra help--see problem below

[eks6426]

Ok you math wiz''s. It''s been a LOOONG time since basic algebra and i was helping my fiance''s son study for his final. We got through everything except one thing. We needed to solve the problem below using the COMPLETING A SQUARE METHOD. I think I got it, but the answer wasn''t available. I remember using the quadratic formula for these kind of problems...can''t recall doing the completing the square method...Can someone do this and let me know the answer...or if you know a website where I can plug in the problem and get the answer that would be great. Thanks!

Here''s the problem--the numbers in RED are exponents:

4a2-8a=24

 

[Catmom]

IslandDreams~

My daughter goes to Winona State University and is pretty much a math Whiz, She says the answer is this........

4((a-1)^2-7)

Hope she''s right! I woudln''t be able to tell because I am lucky to count to 10!

 

[cflutist]

This is what a co-worker had to say about this (he has a Masters of Math from University of California at Davis):

1) Divide the equation by the coefficient of the squared term (4 in this case) giving
a**2 -2a = 6

2) Take one half of the coefficient of "a" (half of -2 is -1) and square it ((-1)*(-1) = +1) and add that to both sides, giving
a**2 - 2a + 1 = 7

3) The left side will now be a perfect square ((a-1)(a-1) in this case). Take the square root of both sides:
(a-1) = sqrt(7) or -sqrt(7) (+ or - 2.645...)

4) Add 1 to each side to get a = 3.645 or - 1.645

Here's more:

(a-1)^2 is a^2 -2a +1. Subtracting 7 gives (a-1)^2 - 7 = a^2 - 2a - 6. Setting this equal to 0 and multiplying by 4 and moving the 24 to the right side does give the original equation. So the "answer" would be

4((a-1)^2-7) = 0 , but this only "completes the square" -- it does not yet say what "a" is. "Solving" means finding the value of "a".

Of course the "4" on the left is worthless.

 

[bopitaddict]

4a2-8a=24

change the a to an x so it follows the usual convention:

4x2-8x=24

quadratic formula uses form:

ax2+bx+c = 0

so putting yours into that:
a=4
b=-8
c=-24

the quadratic solves for x (in your case "a")

x=(-b +/- sqrt(b2-4*a*c))/(2*a)

so...

x=(8+sqrt(64-4*(4)*(-24)))/(2*4) AND x=(8-sqrt(64-4*(4)*(-24)))/(2*4)

so pull our your calculators:

x=(8+sqrt(44)/( AND x=(8-sqrt(44)/(
=(8+8*sqrt(7))/8 AND x=8-8*sqrt(7))/8

which gives you:
x=1+sqrt(7) AND x=1-sqrt(7)

plug it into the calculator and into the original formula and it checks out.

 

[eks6426]

Hey guys--thank you. Cflutist--thanks for typing out the steps. I knew how to do it like bopaddicts''s quadractic formula but the study notes said that it had to be done by completing the square only! I did actually get to the correct answer so I guess that''s pretty good on my rusty algebra skills! I will tell my future step-son tonight and hopefully he will pass his final so we don''t have to do algebra again next year....

 

[MINE!!]

Um.. 2.5?

I am completely clueless in math...

 

[belle]

sorry....just looking at this stuff made me sick.....

i hope there will be no more algebra for you next year!

 

[bopitaddict]

Date: 6/7/2005 3:49:37 PM
Author: IslandDreams
Hey guys--thank you. Cflutist--thanks for typing out the steps. I knew how to do it like bopaddicts''s quadractic formula but the study notes said that it had to be done by completing the square only! I did actually get to the correct answer so I guess that''s pretty good on my rusty algebra skills! I will tell my future step-son tonight and hopefully he will pass his final so we don''t have to do algebra again next year....

dohp... haha... guess that explains why i was never good at reading and english.

 

[AGBF]

We just had to make the decision as to whether our daughter should take algebra or eighth grade math next year. I did not remember algebra as being so hard, but now I am glad we chose eighth grade math!

Deborah

 

[Angel7]

Umm yeah..my calculator is broken so I''m stumped. sorry