Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?

O 12 + V11,2 - V11)

01-2 + V11.-2 - V11]

012+.15.2+7)

x = 2 + √11 or x = 2 - √11

Step-by-step explanation:

I am going to complete the square step-by-step.

x² - 4x - 7=0

Step 1: Add 7 to both sides.

x² - 4x - 7 + 7 = 0 + 7

x² - 4x = 7

Step 2: The coefficient of - 4x is - 4. Let b = - 4.

Then we need to add (b/2) ² = 4 to both sides to complete the square.

Add 4 to both sides.

x² - 4x + 4 = 7 + 4

x² - 4x + 4 = 11

Step 3: Factor left side.

(x-2) ² = 11

Step 4: Take square root.

x - 2 = ±√11

Step 5: Add 2 to both sides.

x - 2 + 2 = 2 ±√11

x = 2 ±√11

x = 2 + √11 or x = 2 - √11