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Mathematics 13 Online
OpenStudy (anonymous):

16x²-8x+1=0

OpenStudy (nathan917):

This a graph question?

OpenStudy (anonymous):

2) 2x²-7x+3=0 3)2x²-x-6=0 4)9x²-3x-2=0 5)y²-6y+2=0 6)4x²-20x+25=0 7)4x²-7x-15=0

OpenStudy (anonymous):

no its not they are solving quadratic equations all of them

OpenStudy (anonymous):

you can solve it by one of the ways used for quadratic equations, like you can try it by using quadratic formula [x=b \pm \sqrt{b ^{2}-4ac}\div2a\]

OpenStudy (anonymous):

i dont know how thats the problem

OpenStudy (anonymous):

can someone help me with it or what

terenzreignz (terenzreignz):

Thankfully, there is the quadratic formula... it's foolproof... you interested? :D

OpenStudy (anonymous):

sure

terenzreignz (terenzreignz):

Well, anytime you're ready, if you have a quadratic equation of the form \[\Large \color{red}ax^2 + \color{blue}bx +\color{green}c = 0\] Where, of course, a is not 0, then the solutions can be quickly obtained using this formula... \[\LARGE x = \frac{-\color{blue}b \pm \sqrt{\color{blue}b^2 - 4\color{red}a\color{green}c}}{2\color{red}a}\] follow this formula (carefully) and you can never go wrong with quadratic equations :D

terenzreignz (terenzreignz):

Let's take the first one as an example... shall we? :)

OpenStudy (anonymous):

okay

terenzreignz (terenzreignz):

\[\Large \color{red}{16}x^2 -\color{blue}8x +\color{green}1 = 0 \] In this case, what are your values for a,b, and c?

OpenStudy (anonymous):

a=15 b=8 and c=1

terenzreignz (terenzreignz):

Where did you get a = 15? lol Also, note the minus-sign preceding the 8... better rethink your value for b.... With those said, what are the values for a,b, and c? :)

OpenStudy (anonymous):

i meant 16 and -8 my fingers and laptop arennt behaving today as you can c

OpenStudy (anonymous):

a=16 b=-8 c=1

terenzreignz (terenzreignz):

LOL, it's fine :) So a = 16 b = -8 c = 1 Great :) So, we plug them into the quadratic formula... \[\LARGE x = \frac{-\color{blue}{(-8)}\pm \sqrt{\color{blue}{(-8)^2}- 4\color{red}{(16)}\color{green}{(1)}}}{2\color{red}{(16)}}\] And just solve :)

OpenStudy (anonymous):

8+-sqrt 64+64/32

OpenStudy (anonymous):

@terenzreignz i dont know exactly how to do this from here

terenzreignz (terenzreignz):

Okay, relax.. deep breaths :D

OpenStudy (anonymous):

lol terenz. dont be so dramatic XD

terenzreignz (terenzreignz):

\[\LARGE x = \frac{\color{blue}{(8)}\pm \sqrt{\color{blue}{64}- \color{red}{64}}}{\color{red}{32}}\] Simplify. :)

OpenStudy (anonymous):

8/32

terenzreignz (terenzreignz):

simplify? :D

OpenStudy (anonymous):

.25

OpenStudy (anonymous):

so both answers are .25

terenzreignz (terenzreignz):

Personally, I prefer 1/4, but whatever floats your boat :P

OpenStudy (anonymous):

yay lol wanna keep helpin me i get the way you talk lol

terenzreignz (terenzreignz):

I haven't said a word :D Okay, do the second one, I'll watch for errors :)

OpenStudy (anonymous):

liar! lol 2x^2-7x+3 a=2 b=-7 c=3 whats the quadratic formula?

terenzreignz (terenzreignz):

\[\LARGE x = \frac{-\color{blue}b \pm \sqrt{\color{blue}b^2 - 4\color{red}a\color{green}c}}{2\color{red}a}\]

OpenStudy (anonymous):

okay so -2+-sqrt2^2-4(-7)(3)/2(2)

OpenStudy (anonymous):

then simplify to get -2=-sqrt88/4 now what? @terenzreignz

terenzreignz (terenzreignz):

Why -2? I thought b = -7 ?

OpenStudy (anonymous):

shooot

OpenStudy (anonymous):

okay hold on i got this

OpenStudy (anonymous):

7+-sqrt25/4 thats right i know

terenzreignz (terenzreignz):

Very good :) Now simplify.

OpenStudy (anonymous):

thats the problem do i actually square it and what do i do with the 7????

OpenStudy (anonymous):

i end up with .5 and 3 when i simplify

terenzreignz (terenzreignz):

YOu got \[\Large \frac{7\pm \sqrt{25}}{4}\]

terenzreignz (terenzreignz):

Which really means... \[\Large \frac{7+\sqrt5}{4} \quad and \quad \frac{7-\sqrt5}{4}\]

OpenStudy (anonymous):

why square root of 5

terenzreignz (terenzreignz):

whoops... sorry replace that with square root of 25 :)

OpenStudy (anonymous):

ok so seven plus 5 and seven -5 divide both by four

terenzreignz (terenzreignz):

Yup :) And those are your answers :D

OpenStudy (anonymous):

3 and .5 i was right okay i need to do this one y^2-6y+2=0

OpenStudy (anonymous):

so a= 1 b=-6 and c=2

terenzreignz (terenzreignz):

Yes. Go ahead :D

OpenStudy (anonymous):

6+5.2915/2=5.14575 6-5.2915/2=.35425

OpenStudy (anonymous):

so 5.2 and.4

terenzreignz (terenzreignz):

I wouldn't suggest approximating... leave it in radical form.

OpenStudy (anonymous):

meaning

OpenStudy (anonymous):

@terenzreignz

terenzreignz (terenzreignz):

Meaning, leave it like this... \[\Large \frac{6\pm \sqrt{36-8}}{2}=\frac{6\pm \sqrt{28}}{2}=\frac{6\pm 2\sqrt7}{2}=3\pm\sqrt7\]

OpenStudy (anonymous):

oh ok

terenzreignz (terenzreignz):

I'm sure you can do the others now :)

OpenStudy (anonymous):

whered 3 come from

terenzreignz (terenzreignz):

We divided by 2 (to get rid of that denominator)

OpenStudy (anonymous):

oh

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