Question

x^2-6x-1=0??

Answer 1

Need quadratic formula or you can try completing the square.

Answer 2

@CliffSedge Completing the square would be redundant here, since he is looking for x, I assume.

Answer 3

its suppose to be completing the square but my ansa isnt coming out like the book

Answer 4

@tyteen4a03 that's why I said, "or" he can do one of the other, they both yield the same result.

Answer 5

it says solve by completing the square but the book have a completely different answer...lost

Answer 6

@CliffSedge But quadratic formula will be much quicker. Since you said "or", oh well.

@Blaque23 Please specify it next time. I will show the first step:
(x - 3)^2 - 9. You take the -6 from -6x, divide it by 2, name it y, then put it into (x + y)^2 (you get what I mean). Now find the square of y (will always be positive) and subtract is from (x + y)^2.

Answer 7

i ike quadratic equations.

Answer 8

my bad its x^2-6x-11=0... and the book has {3+2 square root of 5, 3-2 square root of 5}...how did they get there??

Answer 9

Compare your quadratic equation with \(ax^2+bx+c=0\)
find a,b,c
then the two roots of x are:
\(\huge{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\)

Answer 10

Quadratic formula is *sometimes* quicker. I was able to complete the square in less time than it would have taken to find the discriminant. I depends on the numbers and your mental arithmetic skills.
But that's all irrelevant here.
Fun fact, though: The quadratic formula is derived by completing the square.

Answer 11

\[x^2-6x-11=0 \rightarrow x^2-6x=11 \rightarrow x^2-6x+9 =11+9 \]
\[\rightarrow (x-3)^2=20 \rightarrow x-3=\pm \sqrt{20}.\]
I don't know, I find that easier than plugging a bunch of stuff into the QF and simplifying.
For more complicated numbers, though, QF is definitely the weapon of choice.

Answer 12

getting that number '9' is sometimes not so easy.

Answer 13

where did the 9 come from??

Answer 14

tyteen explained how to get the 9. <scrollup>

Answer 15

Take half the middle coefficient and square it, then add it to both sides.

Answer 16

@Blaque23 My completed-square version of the expression.
@hartnn The general formula for getting that number from (x+h)^2 would be (h/2)^2

Answer 17

n.b. In general, if there is a leading coefficient other than 1 you'd have to factor that out first, then things can get messy with fractions and parentheses and such, so QF is usually preferred in those cases.

Answer 18

that i know,but its not integer always, fraction,
solving in fractions is not considerably easy.

Answer 19

q.v. "...then things can get messy with fractions and parentheses and such,..."

Answer 20

but is that the same as what the book has {3+2√(5), 3-2√(5)}??

Answer 21

ok i got it thanks!!