Question

MEDAL!!!


Completing the square...

Answer 1

\[\large -40 = -6n - 4n^2\]

Answer 2

My steps were:
\[\frac{ -4n^2 - 6n + 40 }{ -4 } = n^2 + 1.5n - 10 \]

\[n^2 + 1.5n -10 = 0 \implies n^2 + 1.5n + (1.5/2)^2 = 10 + (15/2)^2\]

Answer 3

@Nnesha

Answer 4

looks good :=))

Answer 5

Okay so here's the next step:
\[n^2 + 1.5n + 56.25 = 56.25 + 10\]

I know that I need to find the square roots of both sides. And that's where I get the problem.

Answer 6

ohh well here is a short cut
\[\huge\rm x^2 +bx \rightarrow (x+\frac{b}{2})^2 \]
here is an example \[x^2+2x \rightarrow (x+\frac{2}{2})^2 \rightarrow (x+1)^2\]
make sense ??

Answer 7

x+b/2 would be the factor of quadratic equation

Answer 8

What would we do to the "c" term?

Answer 9

let me rewrite it \[\huge\rm x^2+2x +1 \]
factor of this quadratic equation would be (x+b/2)(x+b/2)
which you can write it as (x+b/2)^2

\[(x+\frac{2}{2})(x+\frac{2}{2})=(x+ \frac{2}{2})^2\]

Answer 10

remember the AC method
where we find two numbers when we multiply them we should get product of AC and when we add/subtract them we should get middle term b

Answer 11

we factored it

Answer 12

it's `.5625`

Answer 13

don't i need to make \(\rm n^2 + 1.5n + 56.25\) as a perfect square?

Answer 14

\[n^2 + 1.5n + 0.5625= 0.5625 + 10\]

(1.5/2)^2 = 0.5625

Answer 15

yes right in other words factor that quadratic equation

Answer 16

So I would find the factors of 0.5625? Wouldn't that take some time?

Answer 17

there is a mistake (1.5/2)^2 = 0.5625
not 56.25

Answer 18

Yes sorry

Answer 19

that's why i gave u the shortcutt

Answer 20

when we complete the square:
factor of the quadratic equation would always be \[(x+\frac{b}{2})^2\]

Answer 21

But I don't understand the shortcut. Can we do it with the problem instead of using another example?

Answer 22

sure

Answer 23

\[\color{ReD}{n^2 + 1.5n + 0.5625}= 0.5625 + 10\]
factor of this quadratic equation would always be
\[\large\rm (n+\frac{b}{2})(n+\frac{b}{2})\]
now replace b with its value

Answer 24

\[\rm Ax^2+Bx+C=0\]
quadratic equation where
coefficient of `x term ` is b

Answer 25

\[(n + \frac{ 1.5 }{ 2 })^2\]

Answer 26

\[(n + 7.5)^2\]

Answer 27

looks good
1.5 divide by 2 =.75
so \[\huge\rm (n+.75)^2 = 0.5625+10\]

Answer 28

hmm no 1.5 divide by 2 = 0.75

Answer 29

`0.75 is same as .75`

Answer 30

\[(n+ 0.75)^2 = 10.5625\]

don't i need to find the square root of 10.5625

Answer 31

looks good

Answer 32

yes take square root both sides to cancel out the square

Answer 33

\[n + 0.75 = -3.25 \]
\[n + 0.75 = 3.25\]

Answer 34

perfecT!

Answer 35

I would have to solve for n from both right?

Answer 36

okay gimme a moment...

Answer 37

The answer would be \(\rm 2.4, -4\)?

Answer 38

@Nnesha

Answer 39

hmm i didn't get 2.4

Answer 40

Oh I am sorry. I meant to say 2.5

Answer 41

ah then fantastico!

Answer 42

thank you!

Answer 43

no problema or problemo ..