Solve the Equation...?

Question

Solve the equation e^x(x^2) - 5e^x(x) + 6e^x = 0 for x.

hint: Factor completely and use the fact that e^x>0 for all real values of x.

Not quite sure what I am supposed to do.

10 points

Answer 1

e^x(x^2) - 5e^x(x) + 6e^x = 0

By inspection, you may notice that e^x is the common factor among the three terms on the left side of the equation:

Thus, we can factor it out:

e^x(x^2 - 5x + 6) = 0

Divide both sides by e^x:

x^2 - 5x + 6 = 0

Factor:

(x - 2)(x - 3) = 0

x - 2 = 0

x = 2

x - 3 = 0

x = 3

Solution: x = 2 and x = 3.

Answer 2

you factor out e^x...e^x [ x² - 5x + 6 ] = 0...it should be obvious now

Answer 3

factor out e^x

then x^2-5x+6=0

(x-2)(x-3)=0

x=2 or 3

Answer 4

First factor out one e^x to get a quadratic equation:

e^x(e^x(x)- 5e^x+6)=0

Since e^x >0 that must mean that e^x(x)-5e^x+6=0

Now we have a simple quadratic equation, factoring:

(e^x-2)(e^x-3)=0

e^x= 2 and 3

x=ln(2) or ln(3)

Good Luck!!