I believe that the answer to the square root of x^2 + 3x = x-3 is X = 3, x=-3 but I'm not sure. I believe the answer to the square root of 8x -2 = the square root of 2x is x=2 again I'm not sure.
Square both sides of your equation.
It breaks down quite nicely, but remember that you must verify your answer anytime you squared your equation.
To solve the equation √(x^2 + 3x) = x - 3, you can follow these steps:
1. Square both sides of the equation to eliminate the square root: (√(x^2 + 3x))^2 = (x - 3)^2.
This simplifies to: x^2 + 3x = (x - 3)(x - 3).
2. Expand the right side of the equation: x^2 + 3x = x^2 - 6x + 9.
3. Rearrange the equation to gather like terms: x^2 - x^2 + 3x + 6x - 9 = 0.
4. Combine like terms: 9x - 9 = 0.
5. Add 9 to both sides of the equation: 9x = 9.
6. Divide both sides by 9: x = 1.
So, the solution to the equation is x = 1.
Now let's consider the equation √(8x - 2) = √(2x).
To solve this equation, follow the same steps:
1. Square both sides of the equation: (√(8x - 2))^2 = (√(2x))^2.
This simplifies to: 8x - 2 = 2x.
2. Subtract 2x from both sides: 8x - 2 - 2x = 2x - 2x.
3. Combine like terms: 6x - 2 = 0.
4. Add 2 to both sides: 6x - 2 + 2 = 0 + 2.
5. Combine like terms: 6x = 2.
6. Divide both sides by 6: x = 2/6.
Simplifying the result: x = 1/3.
So, the solution to the equation is x = 1/3.