Question

Determine the solution set of x(squared) + 9x + 20 = 0 by factoring.

Answer 1

Factored form: (x+4)(x+5) = 0

x = -5 or -4

Explanation:

To factor x^2 + 9x + 20, we need to find 2 numbers that multiply to 20 and add up to 9.

The reason for that is because when you multiply (x+a)(x+b) using FOIL, you will get x^2 + ax + bx + ab.

Anyway, 4 and 5 would satisfy this, because 4+5 = 9 and 4*5 = 20. We can then factor the equation to (x+4)(x+5).

To solve (x+4)(x+5) = 0, we need to make either x+4 = 0 or x+5 = 0. That means x can be either -5 or -4.

Answer 2

`x=-4,\:x=-5`

Explanation:

`x^2+9x+20=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}x^2+9x+20:\quad \left(x+4\right)\left(x+5\right)\\\\\left(x+4\right)\left(x+5\right)=0\\\\Using\:the\:Zero\:Factor\:Principle:\\\quad\:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\\\mathrm{Solve\:}\:x+4=0:\quad x=-4\\\\\mathrm{Solve\:}\:x+5=0:\quad x=-5\\\\x=-4,\:x=-5`