Question

Could someone help me solve this equation by completing the square?
6a^2-12a-93=-3

Answer 1

To complete the square \[x^2+ax=0\] we can do the following \[x^2+\frac{ 2ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2=0\]

Answer 2

\[6a^2-12a-90=0\] set it up as such now complete the square

Answer 3

Wouldn't we add 93 to both sides so that we have \[6a ^{2}-12a=90\] ?

Answer 4

then divide -12 by two and square it and add that value to both sides?

Answer 5

So that we have \[6a ^{2}-12a+36=126\]

Answer 6

That's what I have so far

Answer 7

Well I think it would be easiest if you first divide everything by 6 so we have \[6a^2-12a-90=0 \implies a^2-2a-15=0\]\[\left( \frac{ -2 }{ 2 } \right)^2 = 1\] we do this to both sides, but you're essentially right it doesn't matter if you bring it to left or right side. So for simplicity in your case lets put it as \[a^2-2a=15\] now we add the 1 to both sides so we get \[a^2-2a+1=16\]

Answer 8

Now you can easily factor \[a^2-2a+1\]

Answer 9

oh okay that way more simple thanks

Answer 10

Yw :)