Solve each equation by completing the square.
a^2+16-66=-7

Question

Solve each equation by completing the square. 
a^2+16-66=-7

anonymous · Answer

@wolf1728

anonymous · Answer

ok,add 7 to both sides first :)

anonymous · Answer

done

anonymous · Answer

ok you have $\sf \large a ^{2} + 16 - 66 + 7 = 0$

anonymous · Answer

can you say this?
16 - 66 + 7 = ?

anonymous · Answer

yes I do.

anonymous · Answer

nope...

anonymous · Answer

16 - 66 + 7 = -43

anonymous · Answer

so it's $ \sf \large a ^{2} - 43 = 0$

anonymous · Answer

you can solve it by using the formula,or you can solve it by using the laws of mathematics :)

anonymous · Answer

the standard form of these equations are:
$\sf \Large Aa ^{2} + Ba + C = 0$

anonymous · Answer

and the formula is:
$\sf \LARGE a _{1,2} = \frac{ -b \ \pm \ \sqrt{b ^{2}-4ac}}{ 2a }$

anonymous · Answer

can you do it yourself?

anonymous · Answer

so just use the quadratic formula to solve?

anonymous · Answer

yes :)

anonymous · Answer

okay thankyou. I think I can take it from there. :)

anonymous · Answer

and do you want to know how to solve it by the laws of mathematics?
besides that,do you want the proof of this formula?

anonymous · Answer

what does that mean? sorry I'm not good at math...or english... to be honest.

anonymous · Answer

oh no,no problem :)
i'm not good at english too :)
it mean:
$\ \sf \large Every \; equations \; can \; be \; solved \; by \; that \; formula \; or \; by \; the \; laws \; of \; mathematics $
what does "by the laws of mathematics" mean?
i'll tell you :)

anonymous · Answer

$ \sf a ^{2} - 43 = 0$ so can we say $ \sf a ^{2} = 43$  ?

anonymous · Answer

yes we can.

anonymous · Answer

@PFEH.1999

anonymous · Answer

nice :)
please solve this,then you can find you answer:
$\sf a ^{2} = 4$ solve for $ \sf a $

anonymous · Answer

a=2. right?

anonymous · Answer

just 2?

anonymous · Answer

$\sf 2 ^{2} = 4$ it's right

anonymous · Answer

but $\sf(-2)^{2} = 4$ too :)

wolf1728 · Answer

A quadratic function can be solved by 
• factoring 
• the quadratic formula OR 
• completing the square 
Knowing 1 of these methods will allow you to solve all quadratic equations but it seems algebra teachers want to show all 3 ways.

anonymous · Answer

how can you solve$\sf a^{2} = 4 $ by factoring ?:D

wolf1728 · Answer

a² - 4 = 0

anonymous · Answer

it's factoring ???

wolf1728 · Answer

You would be factoring the difference of 2 squares

anonymous · Answer

yes you can say this,but i have another meaning of "Factoring" ...
and now @Mhm120 , got it?
so $\sf (-2)^{2} = 4$ too

wolf1728 · Answer

Now that I think of it, trying to factor 
3x² -17 +23 = 0
would be extremely difficult.

anonymous · Answer

@wolf1728 , we're just confusing him . wait please.

wolf1728 · Answer

Sure as a matter of fact, I think I'll just leave this topic.

anonymous · Answer

no,no your quite right :)
but he know knows the formula,and i wanted to tell him how to solve that by another way,
and you're quite right too.just i said show your work after me :)