can someone explain all the steps from the quadratic to the answer please
#help with this question
mellow bone
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can someone explain all the steps from the quadratic to the answer please
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tropic hazel
can someone explain all the steps from the quadratic to the answer please
It's just completing the square, as well as factoring the leading coefficient.
tropic hazel
i just dont know where the halves n stuff came from
They appear when you factor out 4 after you complete the square. Or before, doesn't matter.
mellow bone
thats the part im not understanding
shouldnt it be 4(x + 4)^2 - 20
i dont know where i went wrong
tropic hazel
thats the part im not understanding
shouldnt it be 4(x + 4)^2 - 20
That is 4x^2 + 32x + 44, so no.
mellow bone
could u walk me through the completing the square process please
tropic hazel
Well, first we look at the quadratic and linear term: 4x^2 + 4x. What does the constant need to be for this to be a perfect square?
mellow bone
4? im not sure what that means...
tropic hazel
No, not 4.
Remember the usual formula: (a + b)^2 = a^2 + 2ab + b^2.
mellow bone
whoa this is new i never learnt that
tropic hazel
You've never learned the square of sum formula?
mellow bone
no i have this different one i think
it is a(x + b)^2 - (1/2b)^2 - c
if that makes sense
neon ravine
can someone explain all the steps from the quadratic to the answer please
take -1 and 4 to other side, use a^2-b^2 = (a+b)(a-b)
tropic hazel
it is a(x + b)^2 - (1/2b)^2 - c
Not sure what this is.
We have:
4x^2 + 4x = (2x)^2 + 2(2x)(1)
So, the constant that makes this a perfect square is 1.
Thus, we get:
4x^2 + 4x = (4x^2 + 4x + 1) - 1
Now, apply the square of sum formula.
mellow bone
ahh this is confusing me, is this what im supposed to know at gcse level?
tropic hazel
What's gcse?
In any case, the square of sum formula should be something you've learned a while ago, since you're solving quadratic equations.
I mean, you use it to derive the quadratic formula.
mellow bone
sorry man ur confusing me
this is the video i used if it makes what im saying any clearer
https://youtu.be/9_2DYOfHxyk?si=A43O4TxOL4GzCmf2
tropic hazel
Well, yeah, the video talks about how to solve quadratic equations by completing the square.
Which is what we are doing.
mellow bone
is it not a different method?
tropic hazel
Different from what?
mellow bone
your method
tropic hazel
There are three main methods of solving quadratic equations:
- Quadratic formula.
- Vieta's formulas.
- Completing the square.
mellow bone
and you were also teaching me completing the square?
how come the video teaches different to what u were saying
tropic hazel
I mean, it's barely different. It doesn't matter.
The approach is to identify what constant term we get based on the quadratic and linear terms.
mellow bone
holdon i think i found where i went wrong
would 4(x + 1/2)^2 - 4/2
be correct
idk how to expand that
tropic hazel
would 4(x + 1/2)^2 - 4/2
Nice! So, we have:
4(x + 1/2)^2 - 4/2 = 0
Next, divide everything by 4 and move the constant to the right side.
mellow bone
x = -1/2 +- (root)1/2
tropic hazel
Great! Those are the solutions.
mellow bone
i understand now thanks