Solve 2x^2 - 8x = -7. I think by completing the square

Question

anonymous · Answer

@Vijeya3 any thoughts?

anonymous · Answer

oh alright thank you so much !

jhonyy9 · Answer

@Everly what is the first step ?

anonymous · Answer

you take the square root right?

jhonyy9 · Answer

no i think take the -7 on the left side and how will get than the quadratic ?

anonymous · Answer

take the -7 and do what?

jhonyy9 · Answer

just than see what you get ?

jhonyy9 · Answer

@Vijeya3 Attention please here in openstudy we dont give to asker directly right answer just we try help step by step - ok ?

anonymous · Answer

I'm still unclear of which route to take, I don't know how to get to the trinomial either

jhonyy9 · Answer

@mathmale your opinion please about this ?

anonymous · Answer

I understand taking the square root, completing the square, quad formula etc

anonymous · Answer

im going to take the quadratic formula i think, and yes ax^2+bx+c=0, right?

anonymous · Answer

i think so but doesn't the x^2 coefficient have to equal to 1?

anonymous · Answer

i tried to divide 2 but that left me with a fraction i didnt know how to solve

anonymous · Answer

are we starting from before or after we add 7 to both sides?

anonymous · Answer

yeah to make it equal to 0

anonymous · Answer

a quadratic formula? 2x^2 - 8x +7 = 0

anonymous · Answer

yes i did it a while ago but forgot it, (x+4) (x-4) ??

anonymous · Answer

so can you explain the method then?

anonymous · Answer

x≈2.70710678,1.29289322

anonymous · Answer

I understand all of that trust me I do and I've done other expressions but its just this one I'm stuck on

anonymous · Answer

@RhondaSommer

rhondasommer · Answer

$$2x^2-8x + 7 = 0$$ this is what you know right?

rhondasommer · Answer

@Vijeya3 i was personally asked to help. please do not interfere while I teach.

anonymous · Answer

Yes, but I don't know where to go after it. I can't use the sum-product, it doesn't make sense

anonymous · Answer

medal?

rhondasommer · Answer

okay Divide each side by '2'.

rhondasommer · Answer

sorry each coefficient

rhondasommer · Answer

because you want the coefficient of x^2 to be 1

anonymous · Answer

i did that but i ended up with the fraction 7/2 (3.5) 
x^2+4+7/2 (3.5) = 0

rhondasommer · Answer

yup :) you need that to continue

rhondasommer · Answer

$$ x^2 - 4x +  3.5= 0$$

rhondasommer · Answer

now; you need to subtract 3.5 from both sides :)

anonymous · Answer

Really? I was trying to complete the square... okay so x^2 +4 = 3.5 what do I do next?

rhondasommer · Answer

$$x^2 + 4 = -3.5$$ not just 3.5 because you subtracted

anonymous · Answer

Oh sorry, I wrote that but didn't type, do I factor?

rhondasommer · Answer

So now your x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

rhondasommer · Answer

$$x^2 + 4 + 4 = -3.5 +4$$

anonymous · Answer

How did you know to do that? What method is that?

rhondasommer · Answer

completing the square.
$$x^2 + 4x + 4 = -3.5 + 4$$

anonymous · Answer

That's the part I'm confused at, because in order to complete square the coefficient of x should be equal to 2a

anonymous · Answer

Which I know see is 2(2) = 4

anonymous · Answer

now*

rhondasommer · Answer

and our x coefficient is 2 so does that make sense now?

anonymous · Answer

Yup! So add 4 to both sides and get x^2 +8 = 7.5, correct?

rhondasommer · Answer

-3.5 + 4 = 0.5.
i also miss wrote it at first
$$x^2+4x+4=-3.5+4$$

anonymous · Answer

This is making so much sense now thank you, okay so , I subtract for now from both sides?

anonymous · Answer

four*

rhondasommer · Answer

nope simplify. ^_^
$$x^2+4x+4=0.5$$$$x^2+4x+4$$ is a perfect square...so simplify it ^_^ then tell me what it is :)

anonymous · Answer

Yup! I just caught on, 

x^2 + 4x + 4
(x+2)^2 
I think, not too sure

rhondasommer · Answer

whoops! i keep writing it wrong. my mistake. $$x^2-4x+4$$ simplify that

rhondasommer · Answer

i made that mistake waaay earlier. it should have been -4x the entire time. luckily that doesnt affect what we have done so far.

rhondasommer · Answer

instead; it will be (x-2)(x-2) = the square root of ±0.5

anonymous · Answer

but would that four we added now have to be subtracted
x^2 - 4x -4 ?

rhondasommer · Answer

no because that is a perfect square ^_^

rhondasommer · Answer

(x-2) = -0.70710678118654752440084436210485 and 
(x-2) =   0.70710678118654752440084436210485

rhondasommer · Answer

simplify those :)

anonymous · Answer

So 2(a) is always 2(a) no matter if x is a negative ?

rhondasommer · Answer

yup :)

rhondasommer · Answer

1.2928932188134524755991556378952
2.7071067811865475244008443621048
when simplified :) does that make sense?

anonymous · Answer

Sorry my computer froze, I'm not sure if I understand how to simplify those. And my options are way different too!

rhondasommer · Answer

thats strange. what are your options

anonymous · Answer

attachment

rhondasommer · Answer

simplify it :)

rhondasommer · Answer

1.4142135623730950488016887242097 is square root of 2

rhondasommer · Answer

and it has to be positive 2 not negative because of (x-2) add two and thats part of your answer

rhondasommer · Answer

so i belive it is d :) √2 /2 is the same as √0.5

rhondasommer · Answer

:) make sense?

anonymous · Answer

I kind of understand that but what do you mean by (x-2) add 2 is a part of my answer?

rhondasommer · Answer

no. x-2 = 0 you have to add 2 two both sides to get x alone

rhondasommer · Answer

its just to get x alone. your answer is simply d

rhondasommer · Answer

::)

anonymous · Answer

I kind of understand that but what do you mean by (x-2) add 2 is a part of my answer?

anonymous · Answer

Oh!!!! Wow I finally get it! I've been on this question since 9 AM and it's now almost 11:30AM. I couldn't figure it out without you @RhondaSommer thank you so so so much :)

rhondasommer · Answer

no problemo ^_^