Solve by completing the square.3u2 + 24u + 27 = 0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.u = or u =

To solve the quadratic equation 3u^2 + 24u + 27 = 0 by completing the square, follow these steps:

Step 1: Divide all terms by 3 to simplify the equation. This gives us: u^2 + 8u + 9 = 0

Step 2: Move the constant term to the other side of the equation: u^2 + 8u = -9

Step 3: Take half of the coefficient of u, square it, and add it to both sides of the equation. Half of 8 is 4, and 4 squared is 16. This gives us: u^2 + 8u + 16 = -9 + 16 u^2 + 8u + 16 = 7

Step 4: The left side of the equation is now a perfect square trinomial, so we can write it as a square of a binomial: (u + 4)^2 = 7

Step 5: Take the square root of both sides of the equation. Remember to consider both the positive and negative roots: u + 4 = sqrt(7) or u + 4 = -sqrt(7)

Step 6: Solve for u: u = -4 + sqrt(7) or u = -4 - sqrt(7)

So, the solutions to the equation are u = -4 + sqrt(7) and u = -4 - sqrt(7).