Question

Complete the square to solve 4x2 + 24x = 4.
0 x=-3+V10
0x=3+ V10
0x=-4+V20
0x=4+ V40

Answer 1

To solve the equation \(4x^2 + 24x = 4\) by completing the square, follow these steps:

1. **Rearrange the equation**:
Start by moving the constant to the other side:
\[
4x^2 + 24x - 4 = 0
\]

2. **Divide the entire equation by 4** (to simplify):
\[
x^2 + 6x - 1 = 0
\]

3. **Move the constant to the right side**:
\[
x^2 + 6x = 1
\]

4. **Complete the square**:
We take half of the coefficient of \(x\) (which is 6), square it, and add it to both sides:
- Half of 6 is 3, and \(3^2 = 9\).

So we have:
\[
x^2 + 6x + 9 = 1 + 9
\]

This simplifies to:
\[
(x + 3)^2 = 10
\]

5. **Take the square root of both sides**:
\[
x + 3 = \pm \sqrt{10}
\]

6. **Solve for \(x\)**:
\[
x = -3 \pm \sqrt{10}
\]

Thus, the solutions can be expressed as:
1. \(x = -3 + \sqrt{10}\)
2. \(x = -3 - \sqrt{10}\)

From your options, the compatible answer is:
- \(x = -3 + \sqrt{10}\)

Given that \(\pm\) implies two solutions, none of the rest are directly matching with typical simplifications of further calculations, so it doesn't appear as any of the other options. But the correct choice from your list is:

\[
x = -3 + \sqrt{10}
\]