Question

Complete the square to solve the following quadratic equation: x2+4x−6=2
. Is the following correct: x=−2+23–√, −2−23–√
?

Enter 1 for Yes.

Enter 2 for No.

(1 point)

Answer 1

Let's complete the square for the equation \( x^2 + 4x - 6 = 2 \).

1. First, rewrite the equation:
\[
x^2 + 4x - 6 - 2 = 0 \quad \Rightarrow \quad x^2 + 4x - 8 = 0
\]

2. Now, move the constant to the other side:
\[
x^2 + 4x = 8
\]

3. To complete the square, take half of the coefficient of \(x\) (which is 4), square it (which gives 4), and add it to both sides:
\[
x^2 + 4x + 4 = 8 + 4
\]
\[
(x + 2)^2 = 12
\]

4. Now, take the square root of both sides:
\[
x + 2 = \pm \sqrt{12}
\]

5. Simplify \( \sqrt{12} \) to \( 2\sqrt{3} \):
\[
x + 2 = \pm 2\sqrt{3}
\]

6. Finally, solve for \(x\):
\[
x = -2 \pm 2\sqrt{3}
\]

The solutions are:
\[
x = -2 + 2\sqrt{3}, \quad x = -2 - 2\sqrt{3}
\]

The provided solutions \( x = -2 + \sqrt{23}, -2 - \sqrt{23} \) are incorrect.

So the answer is:
**Enter 2 for No.**