How do you solve by completing the square for $2x^2 + 2x = 0$ ?

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Answer 1 · 2015-05-16T13:58:51

It's a rather strange way to solve it as it is easy to see that $x=0$ and $x=-1$ are both solutions. However, here's how you would do it...

$0 = 2x^2+2x = 2(x+1/2)^2 - 1/2$

Add 1/2 to both sides to get

$2(x+1/2)^2 = 1/2$

Divide both sides by 2 to get

$(x+1/2)^2 = 1/4$

So

$x+1/2 = +-sqrt(1/4) = +-sqrt(1)/sqrt(2^2) = +-1/2$

Subtract 1/2 from both sides to get

$x=-1/2+-1/2=(-1+-1)/2$

Answer 2 · 2015-05-17T04:03:17

If $2x^2 + 2x = 0$ , then $x^2 + x = 0$ .

To complete this square, I need to square half of the coefficient of the 'x', which is 1/2.

$(1/2)^2=1/4$ , so $x^2 + x + 1/4 = 1/4$

$(x + 1/2)^2=1/4$

$|x + 1/2| = sqrt(1/4)$ (square roots can be positive or negative)

$|x + 1/2| = 1/2$

$x = {-1, 0}$

How do you solve by completing the square for 2x^2 + 2x = 02x^2 + 2x = 0?