Final answer:
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:
- Simplifying equation 1: -3 = -2(12 + 2x).
- Start by multiplying -2 with each term inside the parentheses:
- -3 = -24 - 4x.
- Next, add 24 to both sides to isolate the variable:
- -3 + 24 = -24 - 4x + 24.
- 21 = -4x.
- Lastly, divide both sides by -4 to solve for x:
- 21/-4 = x.
- x = -21/4.
- Simplifying equation 2: -3 = -20(2^2 - 2).
- Start by evaluating the exponent within the parentheses:
- -3 = -20(4 - 2).
- -3 = -20(2).
- Next, multiply -20 with 2:
- -3 = -40.
- But -3 doesn't equal -40, so this equation has no solution.
- Simplifying equation 3: -3 + (-2 √-20x + 12√x) = -20x + 12x^2.
- Combine the like terms on the left side of the equation:
- -3 + (-2 √-20x + 12√x) = -20x + 12x^2.
- -3 - 2 √-20x + 12√x = -20x + 12x^2.
- Now, isolate the variable terms on one side:
- -20x + 12x^2 + 2 √-20x - 12√x = 3.
- Next, rearrange the equation to form a quadratic equation set equal to zero:
- 12x^2 + (-20x + 2 √-20x - 12√x) = 3.
- Lastly, factor or use the quadratic formula to solve for the solutions of x.