Question 1116006
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This is an example of completing the square -- a very useful mathematical tool that you should know.<br>
{{{x^2+y^2+4x-2y+1 = 0}}}<br>
Group the x and y terms on the left and move the constant to the right:<br>
{{{x^2+4x+y^2-2y = -1}}}<br>
Complete the square in both x and y -- that is, add constants (on both sides of the equation, of course!) to make perfect square trinomials in both x and y:<br>
{{{(x^2+4x+4)+(y^2-2y+1) = -1+4+1 = 4}}}<br>
Write the perfect square trinomials as squares of binomials:<br.
{{{(x+2)^2 + (y-1)^2 = 4}}}