Solve the equation for all values of x by completing the square.3, x, squared, plus, 48, x, plus, 189, equals, 03x 2 +48x+189=0

Sure, let's solve the equation step by step:

1. First, write down the equation: 3x^2 + 48x + 189 = 0

2. Divide all terms by 3 to simplify the equation: x^2 + 16x + 63 = 0

3. Now, we need to complete the square. To do this, take the coefficient of x, divide it by 2 and square it. In this case, (16/2)^2 = 64. But our constant term is 63, not 64. So, we need to adjust the equation to make it a perfect square trinomial: x^2 + 16x + 64 - 1 = 0

4. Rewrite the equation: (x + 8)^2 - 1 = 0

5. Now, solve for x: (x + 8)^2 = 1

6. Take the square root of both sides: x + 8 = ± √1

7. Finally, solve for x: x = -8 ± 1

So, the solutions to the equation are x = -9 and x = -7.