What are the solutions to the quadratic equation below?

Question

Answer 1

Completing the square Method :

The equation is 4x² + 28x + 49 = 5.

Separate variables and constants aside by subtracting 49 from each side.

4x² + 28x + 49 - 49 = 5 - 49

4x² + 28x = - 44

Divide each side by 4.

4x²/4 + 28x/4 = - 44/4

x² + 7x = - 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 = 7. So, (half the x coefficient)² = (7/2)²= 49/4.

Add 49/4 to each side.

x² + 7x + 49/4 = - 11 + 49/4

x² + 2(7)(x) + (7/2)² = (- 44 + 49)/4

Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

(x + 7/2)² = 5/4

x + 7/2 = ± √(5/4)

x = - 7/2 ± √5/2

x = (- 7 ± √5)/2.

The option C is correct.