To solve the quadratic equation $x^2 + 2x - 5 = 0$ by completing the square, let's go through the steps:

Step 1: Move the Constant Term

Rewrite the equation by isolating the constant term on the right: $x^2 + 2x = 5$

Step 2: Complete the Square

To complete the square, take half of the coefficient of $x$, square it, and add it to both sides.

1. The coefficient of $x$ is 2.
2. Half of 2 is 1.
3. Squaring 1 gives $1^2 = 1$.

Add 1 to both sides of the equation: $x^2 + 2x + 1 = 5 + 1$ $(x + 1)^2 = 6$

Step 3: Solve for $x$ by Taking the Square Root

Now, take the square root of both sides: $x + 1 = \pm \sqrt{6}$ $x = -1 \pm \sqrt{6}$

Step 4: Approximate the Solutions

Calculating the approximate values: $x \approx -1 + 2.45 = 1.45$ $x \approx -1 - 2.45 = -3.45$

Answer

The solutions, rounded to the nearest hundredth, are: $x = 1.45, -3.45$

For the form in the provided options, select:

• $(x + 1)^2 = 6$

And for the solutions, enter:

• $x = 1.45, -3.45$

Would you like more details on any step? Here are some related questions you might find helpful:

1. How does completing the square differ from other methods for solving quadratic equations?
2. Why do we add the square of half the coefficient of $x$ to both sides?
3. Can completing the square be used for all quadratic equations?
4. How would we solve if the square root resulted in an irrational number?
5. How does this method help in deriving the quadratic formula?

Tip: Completing the square is also helpful for transforming quadratic functions into vertex form, revealing the maximum or minimum values easily.