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 Algebra Pre-Algebra and Basic Algebra Math Forum

 May 6th, 2014, 08:39 AM #1 Newbie   Joined: May 2014 From: sutton coldfield Posts: 11 Thanks: 0 Trial and Improvement Hey, I'm new to this Forum and I'm hoping someone is able to help me I'm currently self teaching Maths GCSE, however I have never come across Algebra before so I'm finding it very tough. My question is as follows; Use trial and improvement to solve the following equations - correct to one decimal place. Show all of your working out. x^2 + x = 100 x^2 - x = 5 x^2 + 2 times = 52 t^3 + t = 2000 Hopefully someone can help me work these out, much appreciated in advance.
 May 6th, 2014, 08:58 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,616 Thanks: 2606 Math Focus: Mainly analysis and algebra First of all, read this article on Trial and Improvement So, all you need to do is to guess values for $x$ until you have fixed $x$ to 1 d.p. So for the first, we know that $10^2 = 100$, so that's a sensible place to start. \begin{align*} \text{Putting $x = 10$ gives} \\ 10^2 + 10 &= 110 \gt 100 &\text{so $x = 10$ is too big, so let's try $x=9$} \\ 9^2 + 9 &= 90 \lt 100 &\text{since 100 is halfway between our attempts so far, let's try $x=9.5$} \\ (9.5)^2 + 9.5 &= 99.75 \lt 100 &\text{we're very close now, so let's try $x=9.55$} \\ (9.55)^2 + 9.55 &= 100.7525 \gt 100 \\ \end{align*} So now we know that the solution $9.5 \lt x_0 \lt 9.55$ which means that $x_0 = 9.5$ to 1 d.p. I'll leave the others for you to try. If you get stuck, post your work so we can help more constructively. The third one is $x^2 + 2x = 52$: $x$ squared plus two times $x$ equals 52. Last edited by v8archie; May 6th, 2014 at 09:04 AM.
 May 6th, 2014, 09:00 AM #3 Newbie   Joined: May 2014 From: sutton coldfield Posts: 11 Thanks: 0 Hi, thanks for posting. It's all to confusing for me the word and term I just don't get.
 May 6th, 2014, 09:05 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,616 Thanks: 2606 Math Focus: Mainly analysis and algebra OK, I had a bit of trouble with formatting, try looking now. If there are terms that you don't understand, tell us which ones they are.
 May 6th, 2014, 09:41 AM #5 Newbie   Joined: May 2014 From: sutton coldfield Posts: 11 Thanks: 0 Hi Again, It sounds stupid, but I just can't get my head around any of it.
 May 6th, 2014, 06:18 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,616 Thanks: 2606 Math Focus: Mainly analysis and algebra Does the equation $$x^2 + x = 100$$ mean anything to you?
 May 6th, 2014, 07:41 PM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002 Why don't you go here: Quadratic Equations "googling" can be VERY helpful...

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