How do you solve x - xe^(5x+2)=0
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How do you solve x - xe^(5x+2)=0

[From: ] [author: ] [Date: 12-01-10] [Hit: ]
by the zero-product property,1 - e^(5x + 2) = 0 ==> e^(5x + 2) = 1 = e^0.5x + 2 = 0 ==> x = -2/5.Therefore, x = -2/5 and x = 0 are the required solutions.I hope this helps!......
By factoring out the x on the left side, we get:
x[1 - e^(5x + 2)] = 0.

So, by the zero-product property, either x = 0 or:
1 - e^(5x + 2) = 0 ==> e^(5x + 2) = 1 = e^0.

Comparing the exponents gives:
5x + 2 = 0 ==> x = -2/5.

Therefore, x = -2/5 and x = 0 are the required solutions.

I hope this helps!
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