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does completing the square and the quadratic formula give same results? watch

1. i was doing some log questions and tried to complete the square of 6x^2 - 28x +16

which gave me x=3 x=1.65 (must have done something super wrong)

and then the quad formula gave me x=4 x=2/3 which is the right answer from markscheme.

this is before i realised i could simplify it and simply factorise, but it made me think do they give different results or did i just do it incorrectly
2. The quadratic formula comes from completing the square on the quadratic . They both give the same answer, because a quadratic always has the same set of solutions.
3. (Original post by ihatePE)
i was doing some log questions and tried to complete the square of 6x^2 - 28x +16

which gave me x=3 x=1.65 (must have done something super wrong)

and then the quad formula gave me x=4 x=2/3 which is the right answer from markscheme.

this is before i realised i could simplify it and simply factorise, but it made me think do they give different results or did i just do it incorrectly
You just completed the square incorrectly.

https://www.thestudentroom.co.uk/sho....php?t=4246394
4. The quadratic formula is just a generalised for of completing the square

x^2 +(b/a)x +(c/a) = 0
(x+(b/2a))^2 +(4ca-b^2)/(4a^2)=0
x+(b/2a) = +-sqrt(b^2-4ac)/2a
x=(b/2a) +-sqrt(b^2-4ac)/2a
5. I second what trythis has said above.

In fact it is very simple to derive the quadratic formula from the general form of a quadratic equation by completing the square. See attachment (apologies for my messy handwriting)
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