Question:
[tex]x^2+5x+6=0[/tex] solve it?
Answer:
[tex]x=-3[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]x= \frac{-b+-sqrt{b^{2}-4ac}}{2a}[/tex]
For a quadratic of the form [tex]ax^{2}+bx+c[/tex].
We have [tex]a=1[/tex], [tex]b=5[/tex], and [tex]c=6[/tex].
[tex]x= \frac{-5+-sqrt{5^{2}-4(1)(6)}}{2(1)}[/tex]
[tex]x= \frac{-5+-sqrt{25-24}}{2}[/tex]
[tex]x= \frac{-5+-sqrt{1}}{2}[/tex]
[tex]x= \frac{-5+-{1}}{2}[/tex]
Hence,
[tex]x= -\frac{6}{2}=-3[/tex] and [tex]x= -\frac{4}{2}=-2[/tex]
You can also factor the quadratic:
[tex]x^2+5x+6=(x+3)(x+2)=0[/tex]
OR
[tex]x^2+5x+6=0\\(x+3)(x+2)=0[/tex]
[tex]x+3=0[/tex]⇒[tex]x=-3[/tex]
and
[tex]x+2=0[/tex]⇒[tex]x=-2[/tex]
