I need help finding x for this equation
e^x (x^2 + 4x + 2)=0
thanks.
e^x = 0 or x^2 + 4x + 2 = 0
the first has no real solution (actually x would have to an infinitely large negative number)
The second is a quadratic, use the formula to solve it.
To find the solutions to the quadratic equation x^2 + 4x + 2 = 0, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 4, and c = 2. So, plugging in these values:
x = (-4 ± √(4^2 - 4*1*2)) / (2*1)
Simplifying this expression gives you two possible solutions for x:
x = (-4 ± √(16 - 8)) / 2
x = (-4 ± √8) / 2
You can simplify the square root of 8:
x = (-4 ± 2√2) / 2
Now, you can simplify further by dividing both the numerator and denominator by 2:
x = -2 ± √2
So, the solutions to the quadratic equation are:
x = -2 + √2
x = -2 - √2
There are no real solutions for the equation e^x (x^2 + 4x + 2) = 0, as the exponential function e^x is always positive and never equal to zero for any real value of x.