Solve by completing the square: −2x^2+24x−40=0

To start this, we want the equation x²+bx+c=0, so we can start by making the x². This would mean that we can divide the whole equation by -2 to get it, resulting in x²-12x+20=0. Next, a formula we have is to, first, divide the -12 by 2, resulting in -6 and (x-6)² due to that to get into the equation x²-12x, we have (x-a)²=x²-2ax+a². As -12=2a, a=-6. After that, we have to see what the result is and adjust based off of that. As we're squaring (x-6)² , we get x²-12x+36, not just x²-12x, so we have to add 36 to both sides to get (x-6)²+20=36. Subtracting 20 from both sides, we get (x-6)²=16. Square rooting both sides, we get x-6=+-√16=+-4. Note that we have the plus or minus due to that for something squared to be a certain number, that something can be positive or negative, e.g. 1²=(-1)²=1. Therefore, if we add 6 to both sides, we get either 10 or 2. 

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