sp;ve by completing the square

Question

4x^2-8x-44=0.

Answer 1

Given equation 4x^2-8x-44 = 0

Take common out 4.

4(x^2-2x-11) = 0

To complete squre we can able to write -11 = -12+1.

4(x^2-2x+1-12) = 0

Divide to each side by 4.

x^2-2x+1-12 = 0

(x-1)^2-12 = 0

Add 12 to each side.

(x-1)^2 = 12

Apply squre root on each side.

√(x-1)^2 = √12

x-1 = √12

Add 1 to each side.

x-1+1 = √12 +1

x = √12 +1

Solutiion x = √12 +1

 

Comments

The solutions of the equation 4x² - 8x - 44 = 0 are x = 1 + 2√3 and x = 1 - 2√3.

Answer 2

The equation is 4x² - 8x - 44 = 0.

Divide each side by 4.

x² - 2x - 11 = 0

Separate variables and constants aside by adding 11 to each side.

x² - 2x = 11.

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = - 2. so, (half the x coefficient)² = (- 2/2)²= 1.

Add 1 to each side.

x² - 2x + 1 = 11 + 1

(x - 1)² = 12

(x - 1)² = (± 2√3)²

x - 1 = ± 2√3

x = 1 + 2√3 and x = 1 - 2√3.

The solutions are x = 1 + 2√3 and x = 1 - 2√3.