title: How to compute system of multivariable equations in Python using Newton-Raphson method?
body: <p>I need your help with programming. Here is my system of equations:</p>
  <pre class="lang-py prettyprint-override"><code>f_1(x1, x2) = 89.3885624 + 169.6377442*x1 + 169.439564*x2 
  + 65.07923*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2)/(2*a2) +0.55071844)/3*x2) 
  + 162.698313*((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2) 
  + 174.39264*x1*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2))/(2*a2) +0.55071844)/3*x2) 
  + 174.39264*x2*((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2) 
  + 72.077218*x1*((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2) 
  + 189.511738*x2*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2)/(2*a2) +0.55071844)/3*x2)
  </code></pre>
  <p>and</p>
  <pre class="lang-py prettyprint-override"><code>f_2(x1,x2) = 78.183644 + 26.71298*x1 + 66.782413*x2 
  - 169.637744*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2)/(2*a2) +0.55071844)/3*x2) 
  - 169.439564*((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2) 
  - 174.39264*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2)/(2*a2) +0.55071844)/3*x2)^2 
  - 261.5889567*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2)/(2*a2) +0.55071844)/3*x2)
  *((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2) 
  - 174.39264*((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2)^2 
  - 54.306279*x1*((-a1-sqrt(a1^2 - 4*a0*a2))/2*a2) 
  + 54.306279*x2*((3*x1*(-a1-sqrt(a1^2 - 4*a0*a2)/(2*a2) +0.55071844)/3*x2)
  </code></pre>
  <p><code>a0</code>, <code>a1</code> and <code>a2</code> are equations with variables <code>x1</code> and <code>x2</code>.</p>
  <p>These two equation needs to be equal to 0 or very close to <code>0</code>. I want to use Newton-Raphson method, but I do not know how. On the internet I find a lot of examples but they use easier system of equation as is mine.</p>
  <p>Sorry for my bad English and thank you for your help!</p>