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CC Math: HSA.REI.B.4, HSA.REI.B.4b

We're asked to
solve the equation 2x squared plus
3 is equal to 75. So in this situation,
it looks like we might be able to isolate
the x squared pretty simply. Because there's only one
term that involves an x here. It's only this x squared term. So let's try to do that. So let me just rewrite it. We have 2x squared
plus 3 is equal to 75. And we're going to try to
isolate this x squared over here. And the best way to do that,
or at least the first step, would be to subtract 3 from
both sides of this equation. So let's subtract
3 from both sides. The left hand side, we're
just left with 2x squared. That was the whole point of
subtracting 3 from both sides. And on the right hand
side, 75 minus 3 is 72. Now, I want to isolate
this x squared. I have a 2x squared here. So I could have just
an x squared here if I divide this side or
really both sides by 2. Anything I do to one side, I
have to do to the other side if I want to maintain
the equality. So the left side, just
becomes x squared. And the right hand side
is 72 divided by 2 is 36. So we're left with x
squared is equal to 36. And then to solve for x,
we can take the positive, the plus or minus square
root of both sides. So we could say the plus or--
let me write it this way-- If we take the square
root of both sides, we would get x is equal to
the plus or minus square root of 36, which is equal
to plus or minus 6. Let me just write
that on another line. So x is equal to
plus or minus 6. And remember here, if something
squared is equal to 36, that something could
be the negative version or the positive version. It could be the
principal root or it could be the negative root. Both negative 6 squared is
36 and positive 6 squared is 36, so both of these work. And you could put them back
into the original equation to verify it. Let's do that. If you say 2 times
6 squared plus 3, that's 2 times 36, which
is 72 plus 3 is 75. So that works. If you put negative
6 in there, you're going to get the
exact same result. Because negative 6
squared is also 36. 2 times 36 is 72 plus 3 is 75.