SOLUTION: {{{ 25y^2-4x^2-8x-104=0 }}} Idk how to find the center teach me please

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Question 1027261: +25y%5E2-4x%5E2-8x-104=0+
Idk how to find the center teach me please
Answer by purpleoj(8) About Me  (Show Source):
You can put this solution on YOUR website!
Okay.
I'm going to start by factoring the -4 away from the "x"s and -104.
+25y%5E2-4%28x%5E2%2B2x%2B26%29=0+
Now, you want to make the X section into a binomial which can be squared easily, and you start by dividing the middle number by 2 and then squaring it to get 1. (sorry if that bit was unclear)
+x%5E2%2B2x%2B1%2B%2825%29+
Now you have 25 left over. This section of your equation now looks like:
+-4%28%28x%2B1%29%5E2%2B25%29+
Multiply the -4 and 25 to get -100 (which I will move to the other end of the equation). Your entire equation now looks like:
+25y%5E2-4%28x%2B1%29%5E2=100+
However, this is not simplified. Now, divide both sides by 100, and you get:
+y%5E2%2F4-%28x%2B1%29%5E2%2F25=1+
If it was just an +x%5E2+, our center would be at the origin (0,0). However, since it is +%28x%2B1%29%5E2+, we subtract 1 from the center x-coordinate out the 1 in +%28x%2B1%29%5E2+. The y-coordinate was unaffected.
Your center coordinate is (-1,0).