must remember completing the square requires to add not subtract. -25+-49+-70 = -144 the negative I was thinking something imaginary. Too much imagination. That perfect square caught my attention and I thought 12= square root of 144
this is the head fake on the -144( the negative square root did catch my attention but it was too delicious to pass up) remember with perfect squares you are adding something to the existing equation so you must add the new value to both sides to make it fair lest you get corrected by the algebra police( who make sure all equations are fair and orderly)who then mark you wrong. If the value already existed on one side of the equation then you could subtract that value from its existing side to nullify it and then subtract it from the other side which is why -144 was so tempting a perfect square as well. However with perfect squares in order to make a more tidy workable solution you have to bring in numbers from the outside and so therefore must make it fair by adding those values in this case 70 to both sides.
But it’s important to remember to subtract on the left (when completing the square for a quadratic) OR to add on the right (when completing the square for a circle). That’s how I try to teach it to my students, anyway.
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Coincidentally enough, we just covered this in Algebra II today. 🙂
must remember completing the square requires to add not subtract. -25+-49+-70 = -144 the negative I was thinking something imaginary. Too much imagination. That perfect square caught my attention and I thought 12= square root of 144
this is the head fake on the -144( the negative square root did catch my attention but it was too delicious to pass up) remember with perfect squares you are adding something to the existing equation so you must add the new value to both sides to make it fair lest you get corrected by the algebra police( who make sure all equations are fair and orderly)who then mark you wrong. If the value already existed on one side of the equation then you could subtract that value from its existing side to nullify it and then subtract it from the other side which is why -144 was so tempting a perfect square as well. However with perfect squares in order to make a more tidy workable solution you have to bring in numbers from the outside and so therefore must make it fair by adding those values in this case 70 to both sides.
I think you mean 74 there at the end, not 70.
But it’s important to remember to subtract on the left (when completing the square for a quadratic) OR to add on the right (when completing the square for a circle). That’s how I try to teach it to my students, anyway.
Mike has written a good question, as usual.