Can someone help me, I am stuck and do not know how to complete. Maybe my first part is wrong, I don't understand by looking at my example if I am doing it right or not.

Square root Property

2k^2 +144=0

2k^2 +144-144=0-144
2k^2=-144
This is where I am confused
2k=sqrt -144 (?)

2k^2 = -144

k^2 = -72

Unless you have studied complex numbers you would stop here and say
"there is no real solution" since you cannot take the square root of a negative.

If you studied complex numbers you should know that i = √-1

so x = √-72
x = ±6√2 i

It looks like you are trying to solve the equation 2k^2 + 144 = 0 using the square root property. Let me guide you through the steps:

1. Start with the equation: 2k^2 + 144 = 0.
2. Subtract 144 from both sides to isolate the term with k^2: 2k^2 = -144.
3. Here is the step where it seems you are unsure. To apply the square root property, you need to take the square root of both sides of the equation.
4. Take the square root of both sides to solve for k: √(2k^2) = ±√(-144).
5. Simplify: √2 * √(k^2) = ±12i.
6. Since the square root of a negative number results in an imaginary number, we use "i" to represent the square root of -1.
7. Simplify further: √2 * k = ±12i.
8. Divide both sides of the equation by √2 to solve for k: k = ±12i/√2.

Therefore, the solution to the equation 2k^2 + 144 = 0 is k = ±12i/√2.