Answer:
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
