Question

Solve the quadratic equation X^2+5x+6=0 using the completing the square method. Be sure to explain each step.

Answer 1

To complete the perfect trinomial, we add (5/2)² to the given equation and get:

`x^2+5x+((5)/(2))^2+6=((5)/(2))^2.`

Subtracting 6 we get:

`x^2+5x+((5)/(2))^2=(25)/(4)-6=(1)/(4).`

Therefore:

`(x+(5)/(2))^2=(1)/(4).`

Finally, we get:

`\begin{gathered} x+(5)/(2)=\pm\sqrt{(1)/(4)}, \\ x=\pm(1)/(2)-(5)/(2). \end{gathered}`

Answer:

`\begin{gathered} x_=-3,\text{ or x=-2.} \\ \end{gathered}`