2(x+4)^2=9 I need to solve using the square root procedure....looking for help in how to work this

Question

whpalmer4 · Answer

$$2(x+4)^2 = 9$$Divide both sides by 2$$(x+4)^2=\frac{9}{2}$$Now take the square root of both sides
$$(x+4) = \pm\sqrt{\frac{9}{2}}$$Can you do the rest?

anonymous · Answer

That's how I had it done but the answer has a -8 in it and I couldn't figure out where it came from

whpalmer4 · Answer

Okay.  Let's go through it.
$$x+4 = \pm\sqrt{\frac{9}{2}}$$$$x = -4\pm\frac{3}{\sqrt{2}}$$Rationalize the denominator by multiplying by $\dfrac{\sqrt{2}}{\sqrt{2}}$
$$x = -4 \pm \frac{3\sqrt{2}}{2} = \frac{-8\pm 3\sqrt{2}}{2}$$

whpalmer4 · Answer

Now does it look the way you expect?

anonymous · Answer

that -8 is still throwing me. I understand -4x2= the -8. but I'm not sure if I saw another problem like this, that I would know what to multiply to get that last part

anonymous · Answer

thank you so much for the help though, it's more clear than it was before :)

whpalmer4 · Answer

yeah, a lot of this is just comfort manipulating fractions and radicals...

whpalmer4 · Answer

not uncommon to end up with the right answer, just in a slightly different form that looks very dissimilar :-)

whpalmer4 · Answer

one thing you can do, assuming your calculator skills are good, is evaluate the expression with a calculator and see if it works out to be the same number.

whpalmer4 · Answer

gotta run, good luck!

anonymous · Answer

Thank you!