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{ (94)/(5)} - 4`
Answer:
The solutions are:

`x = \sqrt{ (94)/(5)} - 4 x = -\sqrt{ (94)/(5)} - 4`