Question

Solve by completing the square:
x^2+2x-7=0

Please help me understand.

Answer 1

Completing the square means you add something to the equation to make it work out to look like \((x + h)^2 = k\) or something of that sort. Then you can just take the square root of both sides.

Answer 2

If it's in the form \(x^2 + bx + c = 0\) this always works out to be half of b, but the process is easier when you think through why this is the case. So if you don't yet understand we can walk through this one.

Answer 3

It make sense, but I would be comfortable talking through it lol, if you don't mind.

Answer 4

Ok. For the time being, ignore the -7. Just think of what will make \(x + 2x + ???\) factor out to \((x + h)^2\). In this case, it's 1, and \(\sqrt{1} = 1\) so we just... add 1.

So add 1 to both sides of the equation.
\[x^2 + 2x + 1 - 7 = 1\]
Then factor.
\[(x + 1)^2 - 7 = 1\]
Then simplify.
\[(x + 1)^2 = 8\]
Now all you have to do to solve it is take the square root. (Remember there is both a positive and negative square root)

Answer 5

Ah, okay. I'm still a bit stuck, So we did simplify but what do you mean by take the sqaure root? lol.

Answer 6

The square root? \(\sqrt{x}\) ?

The square root of n is whatever number you can multiply by itself to get n.

Answer 7

Ohh God, I'm lost lol.

Answer 8

\(\sqrt{9} = 3\) or \(\ -3\) because 3\(\times\)3 = 9 and (-3)\(\times\)(-3) = 9.
Is that familiar?

Answer 9

Yes it is lol.

Answer 10

Ok, so that's what you do here.
\(x + 1 = \pm\sqrt{8}\)

If you're not solid on this stuff you should probably review square roots before you delve too deep into trying to solve quadratics.

Answer 11

Ohhh, You see. It's not that I don't understand. I'm just a different kind of learner, Like i need a teacher to go that extra mile so I can fully understand, but thanks alot man. Appreciate it.