Solve by completing the square. Round to the nearest hundredth if necessary.
3x^2 – 6x – 24 = 0
To solve by completing the square, we first need to isolate the constant term on one side of the equation:
3x^2 - 6x - 24 = 0
3x^2 - 6x = 24
x^2 - 2x = 8
Next, take half of the coefficient of x (-2) and square it:
(-2/2)^2 = (-1)^2 = 1
Add and subtract the square of half the coefficient of x to both sides of the equation:
x^2 - 2x + 1 = 8 + 1
x^2 - 2x + 1 = 9
(x - 1)^2 = 9
Take the square root of both sides:
x - 1 = ± √9
x - 1 = ± 3
Now, solve for x:
x = 1 ± 3
x = 1 + 3 or x = 1 - 3
x = 4 or x = -2
Therefore, the solutions are x = 4 and x = -2.