how do i solve x2 – 2x = 8 by completing the square?
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We generally don't complete the square to solve for a variable. We usually use it to place a quadratic equation into vertex form in order to graph or solve a word problem.
Bring everything to one side
Now we place brackets around the first two terms:
Now we need to create a nice perfect square in the brackets. We do this by taking half of x's coefficient and squaring it. In this case (2/2)^2 = 1 We then add and subtract this number, thereby not "really" changing the equation.
We bring the subtracted term out of the brackets:
Then we factor the bracket:
That would be vertex form (if the 0 was a y)
So if we want to solve:
Square root both sides, this actually gives us a plus and minus version:
so we have two solutions: