Rewrite the equation by completing the square. 4 x^{2} + 20x + 25 = 0

(2x + 5) ² = 0

Step-by-step explanation:

4x² + 20x + 25 = 0

4x² + 10x + 10x + 25 = 0

2x (2x + 5) + 5 (2x + 5) = 0

(2x + 5) (2x + 5) = 0

(2x + 5) ² = 0

(x+5/2) ^2 = 0

Step-by-step explanation:

4 x^{2} + 20x + 25 = 0

Divide by 4

4/4 x^{2} + 20/4x + 25/4 = 0

x^2 + 5x + 25/4 = 0

Subtract 25/4 from each side

x^2 + 5x + 25/4 - 25/4 = -25/4

x^2 + 5x = -25/4

Take the coefficent of x

5

Divide by 2

5/2

Square it

25/4

Add it to each side

x^2 + 5x + 25/4 = -25/4+25/4

(x+5/2) ^2 = 0

Take the square root of each side

x+5/2 = 0

x = - 5/2