Question

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

Answer 1

(2x + 5)² = 0

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

Answer 2

(x+5/2)^2 = 0

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