Final answer:
To solve the equation (3x + 14) = 12, subtract 14 from both sides to isolate the variable, then divide both sides by 3. To solve (2x - 4)^2 = 12, take the square root of both sides and solve for x by adding/subtracting 4 and dividing by 2.
Step-by-step explanation:
To solve the equation (3x + 14) = 12, we can subtract 14 from both sides to isolate the variable. This gives us 3x = -2. Then, we divide both sides by 3 to solve for x. So, x = -2/3.
Now, let's solve the equation (2x - 4)^2 = 12. To do this, we can take the square root of both sides of the equation. Since the square root of 12 is ±√12, we have two equations to solve for x: 2x - 4 = ±√12. Adding 4 to both sides of each equation gives us 2x = 4 ± √12. And finally, dividing both sides by 2 gives us the two possible solutions for x: x = (4 ± √12)/2.