Given:
[tex] x^2+7x+10=0 [/tex]
Since the quadratic equation is equal to 0, we need to solve for x. Let's factor. Since a ≠ 1, we can easily solve. We need to find out what factors of 10 add up to 7. I know that 5*2 = 10 and 5+2 = 7. This fits out problem perfectly. Now that we have that, we can simplify it into two binomials:
[tex] (x+2)(x+5) [/tex]
Now, if it was not equal to zero, we would be done. However, we are not done. We need to set both terms equal to 0 to solve for x.
[tex] x+2=0 [/tex]
To isolate x, subtract 2 from both sides to cancel the +2 on the left.
[tex] x=-2 [/tex]
Let's do the other one:
[tex] x+5=0 [/tex]
Same thing, subtract 5 from both sides to isolate x.
[tex] x=-5 [/tex]
So, in conclusion, your solutions are:
[tex] x=-2 [/tex]
[tex] x=-5 [/tex]
