Given f(x) = x^2 + 8x, what are the values of x when f(x) = 20?
To find the values of x when f(x) = 20, we can set up the equation:
x^2 + 8x = 20
Rearranging the equation, we have:
x^2 + 8x - 20 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. Since the quadratic equation does not factor easily, we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 1, b = 8, and c = -20. Substituting these values into the quadratic formula, we have:
x = (-(8) ± √((8)^2 - 4(1)(-20)))/(2(1))
Simplifying further:
x = (-8 ± √(64 + 80))/2
x = (-8 ± √(144))/2
x = (-8 ± 12)/2
This gives us two possible values for x:
x1 = (-8 + 12)/2 = 4/2 = 2
x2 = (-8 - 12)/2 = -20/2 = -10
Therefore, the values of x when f(x) = 20 are x = 2 and x = -10.