MYTUTOR SUBJECT ANSWERS

317 views

Find the possible values of x for x^2 = 36-5x.

While this question may appear unfamiliar at first, it is just a quadratic equation in disguise. Rearranging such that it equals 0:

x^2 + 5x - 36 = 0

Now this equation is ready to be solved! We can approach this in a couple of ways. I'll go through the factorisation method and using the quadratic formula.

Factorisation Method

This method is often the quickest way but requires a bit of practise to be able to spot the solution. If we look at a general factorisation where the coefficient of x is 1 in both brackets, i.e.

(x+a)(x+b) = 0

We can see when we expand this, we get

x^2 + ax + bx + ab = 0

x^2 + (a+b)x + ab = 0

Going back to our example, this shows us that we need to think of numbers such that a + b = 5 and ab = -36. The tricky part is actually thinking of these numbers.

Because we know that ab is a negative number, we know either a or b must be negative because a negative times a positive is a negative. We now need to trial and error a few potential numbers to find our answers. With a bit of good guessing we can see that a = -4 and b = 9 will work because -4x9 = -36 and -4+9 = 5.

This gives us

(x-4)(x+9)=0

For this to equal zero, one of these brackets must equal 0. If the first one equals 0 then,

x-4 = 0

x=4

or the second one,

x+9=0

x=-9

So our answer is x=4 or x=-9.

If you found it difficult to guess the right numbers then keep practising but, in the meantime, the formula method always works without guessing but does take a little longer...

Formula Method

For a general quadration equation ax^2 + bx + c = 0, the quadratic formula is given by

x = (-b +/- sqrt(b^2 - 4ac))/2a

For our example, a = 1, b = 5 and c = -36, so:

x = (-5 +/- sqrt(25 + (4x36)))/2

x = (-5 +/- sqrt(25+144))/2

x = (-5 +/- sqrt(169))/2

x = (-5 +/- 13)/2

Taking the + option:

x = (-5 + 13)/2

x = 8/2

x = 4

Taking the - option:

x = (-5-13)/2

x = -18/2

x = -9

Therefore, x=4 or x=-9 as expected from our first method.

Ben H. A Level Further Mathematics  tutor, GCSE Further Mathematics  ...

7 months ago

Answered by Ben, a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

466 SUBJECT SPECIALISTS

PremiumRyan G. GCSE Maths tutor, GCSE Physics tutor, GCSE Computing tutor, A...
£22 /hr

Ryan G.

Degree: Electrical Engineering with Renewable Energy (Masters) - Edinburgh University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Computing
-Personal Statements-

“ I will offer a wide range of ways to learn so you can find a way that best suits you!”

Holly R. A Level Biology tutor, GCSE Biology tutor, A Level Chemistry...
£18 /hr

Holly R.

Degree: Medical Sciences (Human Genomics) (Bachelors) - Exeter University

Subjects offered:Maths, Human Biology+ 1 more

Maths
Human Biology

“A tennis coach with 4 years experience teaching, and a passion for it. Studying Medical Science, my enthusiasm allows me to instil the same in others.”

£22 /hr

Runzhi C.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi there, I am an experienced tutor for Biology and Maths. A money-back guarantee is provided if you are not 100% happy with the session. ”

About the author

Ben H.

Currently unavailable: for new students

Degree: Theoretical Physics (Masters) - Birmingham University

Subjects offered:Maths, Science+ 2 more

Maths
Science
Physics
Further Mathematics

“I am a third year Theoretical Physics student at the University of Birmingham. I am passionate about all things physics  and am particularly keen on anything with a strong mathematical element. I am very patient and have a real interes...”

You may also like...

Posts by Ben

Convert the general complex number z=x+iy to modulus-argument form.

Find the possible values of x for x^2 = 36-5x.

Give examples of how the photoelectric effect supports the particle nature of light and defies the wave theory.

What is centripetal force?

Other GCSE Maths questions

What is the cosine rule and when can it be used?

Differentiate (2a+3)^5/2 with respect to a

Solve x^2 + x/2 =5

Express 4/(2-√2) in the form a+b√2 and write down the values of a and b.

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok