Solve the quadratic equation using the square root property: (x+4)^2 = -81

Question

anonymous · Answer

So I set it to 
x^2 = -85 and now I'm confused because it won't take my answer of sqrt85 or -sqrt 85

owlcoffee · Answer

Oh no, my friend.
Uou can't take out the 4 just like that, you have to expand that little (x+4)^2

anonymous · Answer

so should I make it x^2 +16 and then x^2= -97???

owlcoffee · Answer

oh, no no.
Let's do this:
$$(a+b)^{2}$$
This does mean :
$$(a+b)(a+b)$$
Now, let's apply distributive there:
$$a ^{2}+ab+ba+b ^{2}$$
By commutative I know that ab and ba are equal:
then:
$$a ^{2}+2ab+b ^{2}$$
That would be the formula you have to apply, 
Look at your problem, a=x and b=4.
Can you do that?

anonymous · Answer

x^2 +(2x*8) + 16?

anonymous · Answer

x^2+16x+16? So then what do I do with that?

owlcoffee · Answer

solve it for x using sqrt properties :)

anonymous · Answer

So then I'd make it 
x^2 +16x= -97? Oof, I feel like I just keep missing osmething here

owlcoffee · Answer

Hmm... Let's try something.
pass that -81 to the other side as negative, and transform it to a 9^2
Use some exponential properties on those.

anonymous · Answer

sqrtx^2 + sqrt26x + sqrt16 + 9^2 = 0?

anonymous · Answer

I mean to erase the sqrts on those, oops

anonymous · Answer

does x = -13