Hello everyone, I'm Kate and I'm currently in my first year studying Biochemistry at the University of Exeter. I am a member of the canoeing society and enjoy taking part in the training sessions they have on offer. I have had previous experience tutoring GCSE maths whilst studying for my A levels, so am aware of which methods are most effective for explaining topics to ensure understanding. The content covered can be chosen by the student, to focus each session on specific areas. I think it's important to ask any questions in order to be confident with using new skills when solving problems, so if you are unsure about anything either in or between the sessions, feel free to email me. Sessions will normally consist of recapping the previous session to follow up any questions, explaining a new topic by giving examples and model answers, followed by practice questions to work through.
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It is a quadratic equation and when factorised will be of the form (x +/- a) (x +/- b) = 0. We need to find 2 numbers, a and b, that add together to make the 3 for the 3x term and which are multiplied together to give -54 for the constant term. Because the constant is negative (-54), one of the numbers multiplied to give -54 must be negative and the other must be positive as a positive x negative = negative. Possible numbers:
1.(+ or -)1 x (+ or -)54 = -54
2.(+ or -)2 x (+ or -)27 = -54
3.(+ or -)3 x (+ or -)18 = -54
4.(+ or -)6 x (+ or -)9 = -54
We can exclude the first 3 possibilities as it wouldn't be possible to add them together to make +3 (for 3x). This leaves us with (+ or -)6 and (+ or -)9. If we had (-9) + (+6) we would get -3. If we had (+9) + (-6) we would get +3 which is correct.
This means that a= +9 and b= -6
(x + 9) (x - 6) = 0
In order for the above to =0, one of the brackets needs to=0 because any number, n x 0 = 0
Either: x + 9 = 0 which is rearranged to give x= -9 or x - 6 = 0 which is rearranged to give x= 6.
Therefore x= 6 or -9see more