Question

[1. -3 = -2(12 + 2x)]

[2. -3 = -20(2^2 - 2)]

[3. -3 + (-2 √-20x + 12√x) = -20x + 12x^2]

The two solutions are:

A. (x = -5, 1/2)

B. (x = 5, 1/2)

C. (x = -5, -1/2)

D. (x = 5, -1/2)

Answer 1

To solve the given equation step by step, first simplify each expression. Equation 1 results in x = -21/4. Equation 2 has no solution. Equation 3 can be simplified to a quadratic equation to solve for x.

Step-by-step explanation:

To solve the given equation, let's simplify each expression step by step:

1. Simplifying equation 1: -3 = -2(12 + 2x).
2. Start by multiplying -2 with each term inside the parentheses:
3. 
   
4. -3 = -24 - 4x.
5. Next, add 24 to both sides to isolate the variable:
6. 
   
7. -3 + 24 = -24 - 4x + 24.
8. 
   
9. 21 = -4x.
10. Lastly, divide both sides by -4 to solve for x:
11. 
    
12. 21/-4 = x.
13. 
    
14. x = -21/4.
15. Simplifying equation 2: -3 = -20(2^2 - 2).
16. Start by evaluating the exponent within the parentheses:
17. 
    
18. -3 = -20(4 - 2).
19. 
    
20. -3 = -20(2).
21. Next, multiply -20 with 2:
22. 
    
23. -3 = -40.
24. But -3 doesn't equal -40, so this equation has no solution.
25. Simplifying equation 3: -3 + (-2 √-20x + 12√x) = -20x + 12x^2.
26. Combine the like terms on the left side of the equation:
27. 
    
28. -3 + (-2 √-20x + 12√x) = -20x + 12x^2.
29. 
    
30. -3 - 2 √-20x + 12√x = -20x + 12x^2.
31. Now, isolate the variable terms on one side:
32. 
    
33. -20x + 12x^2 + 2 √-20x - 12√x = 3.
34. Next, rearrange the equation to form a quadratic equation set equal to zero:
35. 
    
36. 12x^2 + (-20x + 2 √-20x - 12√x) = 3.
37. Lastly, factor or use the quadratic formula to solve for the solutions of x.