The best method for solving these quadratic equations depends on their structure. Let's analyze each one and choose the most appropriate method:
A. 2a^2 = 72
This is a simple quadratic equation that can be solved by taking the square root of each side:
Divide both sides by 2: a^2 = 36
Take the square root of both sides: a = ±√36
Simplify: a = ±6
B. x^2 - 10x + 16 = 0
This quadratic equation can be factored:
Factor the quadratic: (x - 8)(x - 2) = 0
Use the zero-product property: x - 8 = 0 or x - 2 = 0
Solve for x: x = 8 or x = 2
C. y^2 + 6y = 2
This quadratic equation can be solved by completing the square:
Rearrange the equation: y^2 + 6y - 2 = 0
Complete the square: (y^2 + 6y + 9) - 9 - 2 = 0 (we add (6/2)^2 = 9 to complete the square on the left side)
Factor the left side: (y + 3)^2 - 11 = 0
Solve for y: (y + 3)^2 = 11
Take the square root of both sides: y + 3 = ±√11
Solve for y: y = -3 ± √11
