Question

The first few steps in solving a quadratic equation 5x2+27x=14-13x by completing the square as shown.

Answer 1

For this case we have the following quadratic function
 $5x ^ 2 + 27x = 14-13x$
 To solve by completing squares, we must take into account the following procedures:
 1) The variables on one side of the equation:
 $5x ^ 2 + 27x + 13x = 14 5x ^ 2 + 40x = 14$
 2) The leading term equal to 1:
 $x ^ 2 + 8x = 14/5$
 3) Complete the square:
 $x ^ 2 + 8x + (8/2) ^ 2 = 14/5 + (8/2) ^ 2 x ^ 2 + 8x + (4) ^ 2 = 14/5 + (4) ^ 2 x ^ 2 + 8x + 16 = 14/5 + 16$
 $(x + 4) ^ 2 = 14/5 + 80/5 (x + 4) ^ 2 = 94/5 x = +/- \sqrt{ \frac{94}{5}} - 4$
 Answer:
 The solutions are:
 $x = \sqrt{ \frac{94}{5}} - 4 x = -\sqrt{ \frac{94}{5}} - 4$