Complete the square

[ally1784]

Can someone show me a step to step guide to completing the square for this question please?

[dedformed]

Edit: soz there was initially an error in the last part but I fixed it.



Taking 3 as a common factor for gives



In this case, (5x/3) is the "2ab" term in . Finding "b^2" requires you to halve the coefficient of x and then square it. In this case (5/3) halved is (5/6), squaring it gives (25/36).

Obviously if  just add 25/36 to the previous expression, the vales would change. So you add 25/36 to make a perfect square but also subtract 25/36 to balance it out.




This becomes


 
Now you just simplify



 
You can then solve for x


And

 
Hope this is useful

[ally1784]

Thank you so much, it was clearly explained and very useful. I got a question when completing a square and u take out a factor  such as the example below, how will I know if I need to multiply the number in the bracket because I thought the turning point was (-1,1) but it's actually (-1,4)?

[SmartWorker]

Thank you so much, it was clearly explained and very useful. I got a question when completing a square and u take out a factor  such as the example below, how will I know if I need to multiply the number in the bracket because I thought the turning point was (-1,1) but it's actually (-1,4)?

Hey!

For these type of questions, i usually follow this method:

y= 4x^2 + 8x + 8
y= 4(x^2 +2x) + 8 (leave the 8 out since it doesn't have any x, it won't matter)
y = 4(x^2 + 2x + 1) + 8 - 4 (bc 4x1 = 4 and since you added 4 you must take away 4)
y = 4(x+1)^2 + 4

Now you can say the following from this equation:
1. Dilation by a factor 4 from the x-axis
2. Translation of 1 unit to left and 4 units up

We don't factorise the 4 out bc its a dilation from the x-axis.

Hope this helps!