
Algebra PreAlgebra and Basic Algebra Math Forum 
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May 6th, 2014, 09:39 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, 09:58 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 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 10:04 AM. 
May 6th, 2014, 10:00 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, 10:05 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 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, 10:41 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, 07:18 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
Does the equation $$x^2 + x = 100$$ mean anything to you? 
May 6th, 2014, 08:41 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,459 Thanks: 949  

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