what are the solutions to the equation
z^2 - 6z - 27 = 0 there are two solutions, and the options available are 3, -3, 9, and -9
well, geez, did you try them?
Or, note that you want (z-9)(z+3) = 0
oh yeah me answer was 3, -9, but that doesn't feel right, or it may just be me
oh so its -9, 3?
oh wait, -9, 3 isnt an answer,um, is it -3, 9?
now im confused
yeah all of the answers start with either 3 or -3
To find the solutions to the equation z^2 - 6z - 27 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing this with our equation, we have a = 1, b = -6, and c = -27. Now we can substitute these values into the quadratic formula and solve for z:
z = (-(-6) ± √((-6)^2 - 4(1)(-27))) / (2(1))
Simplifying further:
z = (6 ± √(36 + 108)) / 2
z = (6 ± √(144)) / 2
z = (6 ± 12) / 2
This gives us two possible solutions:
z1 = (6 + 12) / 2 = 18 / 2 = 9
z2 = (6 - 12) / 2 = -6 / 2 = -3
Therefore, the solutions to the equation z^2 - 6z - 27 = 0 are z = 9 and z = -3.
Given the options of 3, -3, 9, and -9, the correct solutions are 9 and -3.