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