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\[\log_{2}x ^{2}+x-52=2 \]

|dw:1433299192056:dw|

|dw:1433299285026:dw|

Then I used the quadratic formula to get \[\frac{ -1\pm \sqrt{217} }{ 2}\]

But my homework program has rejected all of my answers so I'm at a bit of a loss

You were on the right track at \(\rm \color{purple}{x^2+x-52=4}\)

Give me a minute

Well, now you just want to solve it
Oh, and do you know how many solutions you will have?

I think that the problem is with the number in the square root.

Not exactly, but there's at least one.

Yes, there is 2 solutions for x

Are they asking you to solve for x?

Ok, so continue. Can you tell me what you got when you finish?

x=7,-8

Just checked it in my program and it's correct.

Right :)

I can't figure out for the life of me where my calculator came up with 217 instead of 225

Hmm, are you using like a calculator on your computer or..?

Yes, so I used a different one which is where I got the correct answer.