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May 6th, 2014, 09:39 AM   #1
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From: sutton coldfield

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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.
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May 6th, 2014, 09:58 AM   #2
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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.
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May 6th, 2014, 10:00 AM   #3
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Hi, thanks for posting.

It's all to confusing for me the word and term I just don't get.
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May 6th, 2014, 10:05 AM   #4
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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.
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May 6th, 2014, 10:41 AM   #5
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Hi Again,

It sounds stupid, but I just can't get my head around any of it.
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May 6th, 2014, 07:18 PM   #6
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Does the equation
$$x^2 + x = 100$$
mean anything to you?
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May 6th, 2014, 08:41 PM   #7
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Why don't you go here:
Quadratic Equations

"googling" can be VERY helpful...
Denis is offline  
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