Question

Solve x^2 - 4x - 7 = 0 by completing the square. What are the solutions?

Answer 1

Answer:

x = ±√11 +2

Step-by-step explanation:

Given in the question an equation,

x²- 4x - 7 = 0

Step 1

take 7 to the right side of equation

x²- 4x = 7

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b, the coefficient of x

2ab = -4x

2xb = -4x

b = -2

Step 3

Take square of b and add it to each side of the equation.

x²- 4x + (-2)²= 7 + (-2)²

x²- 4x + 4 = 7 + 4

x²- 4x + 4 = 11

Step 4

Factor the perfect trinomial square

(x−2)² = 11

Step 5

take square root on both sides

√(x−2)² = √11

(x-2) = ±√11

x = ±√11 +2

Answer 2

Answer:

x = 2 - √11

x = 2 + √11

Step-by-step explanation:

We can see the solution to your question in the attached pictures below

If we complete squares, we get

x^2 - 4x - 7   + 4  =  + 4

x^2 - 4x  + 4  =  + 4 + 7

(x -2)^2  = 11

x = 2 ±√11