Question

Complete the square for 3x2 - 12x = 9.
0(3x-212=20
0(x-212=7
0(3x-2)2= 13
0(x+212=7

Answer 1

Let's start from the equation you provided:

\[ 3x^2 - 12x = 9. \]

To complete the square, we can follow these steps:

1. **Move the constant term to the other side**:
\[
3x^2 - 12x - 9 = 0.
\]

2. **Factor out the coefficient of \(x^2\) from the \(x\) terms**:
\[
3(x^2 - 4x) = 9.
\]

3. **Complete the square on the expression inside the parentheses**:
To complete the square for \(x^2 - 4x\), we take half of the coefficient of \(x\) (which is \(-4\)), square it, and add it inside the parentheses. Half of \(-4\) is \(-2\), and squaring it gives \(4\).

Thus,
\[
3(x^2 - 4x + 4 - 4) = 9,
\]
which we can rewrite as:
\[
3((x - 2)^2 - 4) = 9.
\]

4. **Distributing the \(3\)**:
\[
3(x - 2)^2 - 12 = 9.
\]

5. **Add \(12\) to both sides**:
\[
3(x - 2)^2 = 21.
\]

6. **Divide through by \(3\)**:
\[
(x - 2)^2 = 7.
\]

So, after completing the square, the equation is:
\[
(x - 2)^2 = 7.
\]

This is the completed square form of the original equation.