Quadratic Equations math help!!?

Question

1) Solve 16x^2 - 25= 0 

2) Solve (x-3)^2= 4 

3) Solve by completing the square: 

x^2 + 12x +16 = 0

Answer 1

1).

The quadratic equation is 16x^2 - 25 = 0.

16x^2 = 25

x^2 = 25/16

x^2 = (± 5/4 )^2

Extract square root from each side.

x = ± 5/4.

Te solutions of the quadratic equation are x = 5/4 and x = - 5/4.

2).

The quadratic equation is (x - 3)^2 = 4.

(x - 3)^2 = (± 2)^2

Extract square root from each side.

x - 3 = 2 and x - 3 = - 2

x = 2 + 3 and x = - 2 + 3

x = 5 and x = 1.

The solutions of the quadratic equation are x = 5 and x = 1.

3).

The quadratic equation is x² + 12x + 16 = 0.

Separate variables and constants aside by subtracting 16 to each side.

x² + 12x = - 16

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

 Here x coefficient = 12. so, (half the x coefficient)² = (12/2)²= 36

Add 36 to each side

x² + 12x + 36 = - 16 + 36

(x + 6)²= 20

Take square root both sides.

x + 6 = ± √20

x = - 6 ± √20.

The solutions of the quadratic equation are x = - 6 + √20 and - 6 - √20.