Answer:
See below
Step-by-step explanation:
Hi there!
Mai was given the equation x²+7x=0, and rewrote it as x(x+7)=0 to help solve it
Rewriting the equation in this way helps Mai solve the equation is because it helps make sure none of the answers are missing.
If you look at the equation x²+7x=0, you might think that you are able to divide both sides by x, and then solve x+7=0.
However, this method is incorrect.
The answer to x+7=0 would be x=-7, which if you plug -7 as x into the equation, it would show that it is a correct answer, but it is not the only correct answer.
If you plugged 0 into the equation as well, here is what would happen:
(0)²+7(0)=0
Raise 0 to the second power and multiply 7 by 0
0 + 0 = 0
Add the numbers together
0=0
As you can see, x=0 is also a correct answer to the equation.
However, if you had divided x from both sides, you wouldn't have been able to find that x can also equal 0.
If we factored the equation as Mai did it, x(x+7)=0, then by zero product property, x would equal both 0 <em>and </em>7
As you can see, both answers are there if we had factored it Mai's way, and none of the answers are missing.
Hope this helps!
