How do you solve x2+5x+6=0 by factoring?

3 Answers
Jim G.
Jul 16, 2018

x=−3 or x=−2

Explanation:

the factors of +6 which sum to +5
are +3 and +2

(x+3)(x+2)=0

equate each factor to zero and solve for x

x+3=0⇒x=−3

x+2=0⇒x=−2

Sonnhard
Jul 16, 2018

x=−2 or x=−3

Explanation:

Completing the square

x2+2⋅52x+254+6−254=0

we get

(x+52)2−14=0

using that a2−b2=(a+b)(a−b)

we get
(x+52−12)(x+52+12)=0

so (x+2)(x+3)=0

we get x=−2 or x=−3

Jacobi J.
Jul 16, 2018

x=−2 and x=−3

Explanation:

Let's do a little thought experiment:

What two numbers sum to the middle term, and have a product of the last term?

After some trial and error, we arrive at 2 and 3. This means we can factor this as

(x+2)(x+3)=0

Next, we can set both factors equal to zero to get

x=−2 and x=−3

Hope this helps!

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