solve the following by completing the square
2x^2-24x=0
a. x=-18;-6
b. x=0;12
c.x=6;18
d. x=-12;0
To solve by completing the square, we first need to put the equation in the form of ax^2 + bx + c = 0.
Given the equation: 2x^2-24x = 0
To complete the square, divide every term by 2: x^2 - 12x = 0
Now, add and subtract (b/2)^2 to the equation: x^2 - 12x + 36 = 36
This equation can be rewritten as: (x-6)^2 = 36
Now, take the square root of both sides: x - 6 = ±6
Solve for x: x = 6 ± 6
This gives us two solutions: x = 6 + 6 = 12 and x = 6 - 6 = 0
So, the correct answer is: b. x=0;12