Solve the equation using the quadratic formula.

negative lower x squared plus 27 equals 6 lower x
(1 point)
Responses

lower x equals negative 3 comma lower x equals 9
Image with alt text: lower x equals negative 3 comma lower x equals 9

lower x equals negative 3 comma lower x equals 3
Image with alt text: lower x equals negative 3 comma lower x equals 3

lower x equals negative 9 comma lower x equals 9
Image with alt text: lower x equals negative 9 comma lower x equals 9

lower x equals negative 9 comma lower x equals 3
Image with alt text: lower x equals negative 9 comma lower x equals 3
Remainin

1 answer

g focused on the general form of the equation, we have:

- x^2 + 27 = 6x

First, rearrange the equation to set it equal to zero:

- x^2 - 6x + 27 = 0

Now, plug the coefficients into the quadratic formula:

x = [ -(-6) ± √((-6)^2 - 4(1)(27)) ] / 2(1)
x = [ 6 ± √(36 - 108) ] / 2
x = [ 6 ± √(-72) ] / 2
x = [ 6 ± 6√3i ] / 2
x = 3 ± 3√3i

The two possible solutions are x = 3 + 3√3i and x = 3 - 3√3i.