Maths Homework

[GlenB]

Am trying to help with my grandson’s homework. Part of one question requires him to solve the equation 2x - 2x² = 0.24
By trial and error I have calculated that x = 0.139 but could some kind person show me how to solve this algebraically please.
Thanks.

[mathsanswer2]

It's very difficult to show you the algebra here, as i cannot seem to insert the correct mathematical symbols, but i'll try.
2x - 2x² = 0.24 this is a quadratic equation that cannot be factored, so using the formula x = b + or - square root of b² -4ac all divided by 2a you will be able to do it. First you rearrange your original formula to get
-2x² +2x - 0.24 = 0.
(i.e. ax² -bx - c = 0)
then substitute into the formula for x above so a= -2 b=2 and c=-0.24. This gives two possible solutions and you get the answers x = 0.14 (which is the 0.139 you suggest) or x= 0.86. If you use these two answers in the formula, you will see they are both correct.
Apologies that this is difficult to understand, but it's very difficult without the ability to draw the maths formulas correctly.
If the above is not clear, then google "how to solve quadratic equations that cannot be factored" and you'll be able to see the formulas, and will be on the right track.

[The Builder]

Quadratic formula halfway down on the right..........

http://www.regentsprep.org/Regents/math/algtrig/ATE3/QuadLesson.htm

[Prudie]

Just to add from 1st post the formula starts with x = - b +/- etc and is clear in thebuilder's link. However if you are doing it by trial and error and your grandson didn't stop you it suggests he has no idea of the existence of the formula so I've no idea why he'd be set this problem - unless he's missed some classes?

[bert_h]

2x^2 - 2x = -0.24 (by reversing the signs)
4x^2 - 4x = -0.48 (by multiplying by 2)
4x^2 - 4x + 1 = 0.52 (by adding 1 to each side)
(2x - 1)^2 = 0.52
2x - 1 = +- 0.7211102 (by taking square roots)
2x = 1.7211102 or 0.2788898
x = 0.8605551 or 0.1394449

[Prudie]

Well done bert-h but if he can't do it by formula it's highly unlikely he could do it by completing the square :-)

[factor-fiction]

If the quadratic formula is to be used I think it's easier to rewrite it as
x²-x+0.12=0

I also like bert's approach of 'completing the square'.

[factor-fiction]

Completing the square is regarding as grade A/A* stuff now and I only ever use with the students who are fully familiar with factorising and using the quadratic formula (which is A or B I recall). The quadratic formula is now provided to students on the exam paper

[GlenB]

Thanks to all of you for your help.

[vascop]

Although all these methods are mathematically correct that are not very insightful, especially for a young person. Surely what the question is looking for is to write this as "find the points of intersection of y=2x-2x^2=x(1-x) and y=0.24" whixh is done by drawing the graph of each on the same sheet and look for the points of intersection.

[vascop]

oops.. should be "...they are not very insightful..."

[vascop]

or even better y=x^2 and y=x-0.12