Solve by completing the square. Round to the nearest hundredth if necessary.%0D%0A%0D%0A3x2 – 6x – 24 = 0
Starting with the equation 3x^2 - 6x - 24 = 0:
Step 1: Divide by the coefficient of x^2, which is 3.
x^2 - 2x - 8 = 0
Step 2: Move the constant term to the other side of the equation:
x^2 - 2x = 8
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - 2x + 1 = 8 + 1
(x - 1)^2 = 9
Step 4: Take the square root of both sides:
x - 1 = ±3
x = 1 ± 3
Therefore, the solutions are x = 1 + 3 and x = 1 - 3, which simplifies to x = 4 and x = -2.