Question

What are the solutions to the equation x^2+9x+12=6

Answer 1

`x= -\frac {9}2 +(√(57))/(2),~~x = -\frac {9}2 - (√(57))/(2)`

Explanation:

`~~~~~~~x^2 +9x +12 = 6\\\\\implies x^2 +9x = 6-12\\\\\implies x^2 +9x = -6\\\\\implies x^2 +2 \cdot \frac 92 \cdot x +\left(\frac 92\right)^2 -\left( \frac 92 \right)^2 = -6\\\\\implies \left(x+ \frac 92 \right)^2 -(81)/(4)= -6\\\\\implies \left(x +\frac 92 \right)^2 = -6 + \frac{81}4\\\\\implies \left(x + \frac92 \right)^2 = (57)/(4)\\\\\implies x+ \frac 92 = \pm\sqrt{\frac{57}4}\\\\\implies x = -\frac {9}2 \pm(√(57))/(2)`