Question 968469
Change the equation to standard form
x^2+ y^2 - 2x + 14y + 1 = 0
<pre>
{{{x^2+ y^2 - 2x + 14y + 1}}}{{{""=""}}}{{{"0"}}}

Get the like letter terms together and subtract the constant term from
both sides:

{{{x^2 - 2x + y^2 + 14y }}}{{{""=""}}}{{{-1}}}

Put parentheses around the x terms and the y terms,
skipping a space after each:

{{{(x^2 - 2x+matrix(1,3,"","","")) + (y^2 + 14y+matrix(1,3,"","","")) }}}{{{""=""}}}{{{-1}}}

Complete the square in the first parentheses:
1. Multiply the coefficient of x, which is -2 by 1/2, getting -1
2. Square -1.  (-1)<sup>2</sup>, getting +1
3. Add it in the space in the first parentheses, and also add it
to the right side:

{{{(x^2 - 2x+1) + (y^2 + 14y+matrix(1,3,"","","")) }}}{{{""=""}}}{{{-1+1}}}

Complete the square in the second parentheses:
1. Multiply the coefficient of x, which is 14 by 1/2, getting 7
2. Square 7.  (7)<sup>2</sup>, getting +49
3. Add it in the space in the second parentheses, and also add it 
to the right side:

{{{(x^2 - 2x+1) + (y^2 + 14y+49) }}}{{{""=""}}}{{{-1+1+49}}}

Factor each parentheses and combine numbers on the right:

{{{(x-1)(x-1)+(y+7)(y+7)=49}}}

Write the factorizations as squares:

{{{(x-1)^2+(y+7)^2=49}}}

Edwin</pre>