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Completing sq for Quadratic expressions

Hi,

I am just working through an exercise on completing the square for quadratic expressions.

I have seemed to get the content and how to complete a square for a quadratic function up until now..

I think I am making a silly mistake somewhere and so my answers are slightly wrong - I am awful at factorisation so it may be that. Anyway, could somebody please explain the answer to this question, complete the square for:

a) 2x^2 -6x+5
My answer: 2((x-3/2)^2-11/4
Correct answer: 2((x-3)^2+1/2

I guess I'm not simplifying enough but I if I were wouldn't I get 2 and 3/4? Where is the 1/2 coming from??

b) 5+4x-2x^2
My answer:
factorise = 2(x^2-2x+5/2)
complete sq. = 5-1-2(x-1)^2 therefore 4-2(x-1)^2
BUT, correct answer is 7-2(x-1)^2; where is the 7 coming from?

I think I'm following the method ok but am making mistakes somewhere in the working out which is giving me the wrong answer.

Any help would be hugely appreciated!! Thank you

Reply 1

TenOfThem

Original post by Aimee1989

a) 2x^2 -6x+5
My answer: 2((x-3/2)^2-11/4
Correct answer: 2((x-3)^2+1/2

Hmmmm

2x^2 - 6x + 5 = 2[x^2 - 3x + \frac{5}{2}] = 2[(x-\frac{3}{2})^2 - \frac{9}{4} + \frac{10}{4}] = 2(x-\frac{3}{2})^2 + \frac{1}{2}

Did you miss a bit out of their answer
Can you see where you went wrong

Reply 2

TenOfThem

Original post by Aimee1989

b) 5+4x-2x^2
My answer:
factorise = 2(x^2-2x+5/2)

5 + 4x - 2x^2 = -2[x^2 - 2x - \frac{5}{2}]

Reply 3

BabyMaths

Alternatively, write the answer in terms of unknown constants, expand and compare coefficients.

Eg.

2x^2-6x+5=2(x-a)^2+b

=2x^2-4ax+2a^2+b

-4a=-6 \\ 2a^2+b=5

Reply 4

BabyMaths

Original post by Aimee1989

That's wrong so it's good that you didn't get that.

Reply 5

Aim456

Original post by BabyMaths

That's wrong so it's good that you didn't get that.

That is the answer that is given in the textbook...

Reply 6

TenOfThem

Original post by Aimee1989

That is the answer that is given in the textbook...

Are you sure that it isn't the answer I gave in post 2

Reply 7

Aim456

Original post by TenOfThem

Hmmmm

2x^2 - 6x + 5 = 2[x^2 - 3x + \frac{5}{2}] = 2[(x-\frac{3}{2})^2 - \frac{9}{4} + \frac{10}{4}] = 2(x-\frac{3}{2})^2 + \frac{1}{2}

Did you miss a bit out of their answer
Can you see where you went wrong

Hi, thanks for this! I guess I added rather than subtracted (foolish) to give 11/4 rather than 1/4 (-9/4+10/4) but how and when does that become 1/2??
thanks

Reply 8

Aim456

Original post by TenOfThem

Are you sure that it isn't the answer I gave in post 2

Ah yes, sorry! I didn't realise I had wrote (x-3)^2 thought I had wrote (x-3/2)^2

I managed to get that bit but somehow came out with 11/4 rather than 1/2 - I assume i'm just being a bit dim and not simplifying or something?

Reply 9

TenOfThem

Original post by Aimee1989

Hi, thanks for this! I guess I added rather than subtracted (foolish) to give 11/4 rather than 1/4 (-9/4+10/4) but how and when does that become 1/2??
thanks

When you multiply it by 2

Reply 10

Aim456

Original post by TenOfThem

When you multiply it by 2

Oooooh!! Of course. I've been leaving the end numbers as they are and not multiplying out by the term outside of the bracket. Ah.. A moment of clarity; this could be why all of my answers seem to be slightly wrong! Ha. I need to look at the equation properly from now on I guess..

Thank you so much!