Solve the quadratic equation by factoring:
k²+4k=0
ANSWER:
To solve this quadratic equation by factoring, we need to find two numbers that multiply to 0.
k²+4k=0
We can factor out k:
k(k+4)=0
Now we have two factors, k and k+4, that multiply to 0. This means that either k=0 or k+4=0.
If k=0, then the equation becomes:
0²+4(0)=0
This is true, so k=0 is a solution.
If k+4=0, then k=-4. Substituting this into the equation, we get:
(-4)²+4(-4)=0
This is also true, so k=-4 is another solution.
Therefore, the solutions to the quadratic equation k²+4k=0 are k=0 and k=-4.
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