Sqrt -8x+6-3=8x... I need help solving !

Question

oaktree · Answer

Do you mean$$\sqrt{-8x+6} -3 = 8x$$

anonymous · Answer

http://www.wolframalpha.com/input/?i=Sqrt+-8x%2B6-3%3D8x

anonymous · Answer

Yes , I need all possible solutions .

oaktree · Answer

@Gabriel.Dalbani, stop just plugging things into WolframAlpha.

oaktree · Answer

So what you need to do to solve, @Shgre17, is first move the -3 over to the right-hand side of the equation and then square both sides. So it should look like this:$$-8x + 6 = (8x + 3)^2$$

oaktree · Answer

Following so far?

oaktree · Answer

And thanks for the medal, @CGGURUMANJUNATH. I appreciate it.

anonymous · Answer

Yes

cggurumanjunath · Answer

you're welcome @OakTree

oaktree · Answer

Great. So then we FOIL out the right hand side. Can you do that?

anonymous · Answer

Yes I can, give me a sec to do the math @oaktree

cggurumanjunath · Answer

wolfram alfa plugging directly gives wrong answer interpreting would be difficult.

anonymous · Answer

After you foil you would end up with 16x^2+24x+24x+9 right?

oaktree · Answer

Not quite. Your first term is wrong.

oaktree · Answer

You see your mistake?

anonymous · Answer

Lol sorry its 64x^2

oaktree · Answer

Yeah. Now add the two middle terms and you get...?

anonymous · Answer

48x

oaktree · Answer

Right. So we have$$-8x + 6 = 64x^2 + 48x + 9$$Now combine like terms so we have a quadratic equation. We get$$64x^2 + 56x + 3 = 0$$Which doesn't factor nicely, so we have to use the quadratic formula. Do you know it?

anonymous · Answer

It's ax^2+bx+c right ?

oaktree · Answer

Not quite. The quadratic formula is $$x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }$$

anonymous · Answer

Okay , so what do I do next?

oaktree · Answer

Well, you take the values for a, b, and c from your equation and plug them in. The two answers you get (since it's plus and minus) are your roots. Okay?

oaktree · Answer

So it would go like this:$$x = \frac{ -56 \pm \sqrt{56^2 - 4(64)(3)} }{ 2(3) }$$

anonymous · Answer

Okay I have that

oaktree · Answer

Which, simplified, is $$\frac{ -56 \pm 8 \sqrt{37} }{ 6 }$$

oaktree · Answer

Now, do you think you can simplify that all the way and get your answers?

anonymous · Answer

How did you get that ?

oaktree · Answer

Simplify the inside of the square root.