What are the solution sets of the following 3 problems,the square root of x squared + 3x = x-3, the square root of 3x + 10 = x + 4 and finally the square root of 8x - 2 = the square root of 2x? Help much appriciated.
I will one as an example.
sqrt(3x + 10) =x+4 I hope that is what you meant. When you don't use parenthesis in problems it can lead ot miscommunications.
square both sides:
3x + 10 = x^2 + 8x + 16
gathering terms then
x^2 + 5x +6 =0
(x+3)(x+2)=0
x= -2 9r x=-3
I will be happy to critique your work thinking on the others.
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.
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.
To find the solution sets for the equations, let's work through them step by step.
1. sqrt(x^2 + 3x) = x - 3
Square both sides:
x^2 + 3x = (x - 3)^2
x^2 + 3x = x^2 - 6x + 9
Simplify and gather like terms:
6x = 9
x = 9/6
x = 3/2
So, the solution to this equation is x = 3/2.
2. sqrt(3x + 10) = x + 4
Square both sides:
3x + 10 = (x + 4)^2
3x + 10 = x^2 + 8x + 16
Rearrange the terms:
x^2 + 5x + 6 = 0
Factorize the quadratic equation:
(x + 2)(x + 3) = 0
Set each factor equal to zero:
x + 2 = 0 or x + 3 = 0
Solve for x:
x = -2 or x = -3
So, the solutions to this equation are x = -2 and x = -3.
3. sqrt(8x - 2) = sqrt(2x)
Square both sides:
8x - 2 = 2x
Rearrange the terms:
8x - 2x = 2
Combine like terms:
6x = 2
Solve for x:
x = 2/6
x = 1/3
So, the solution to this equation is x = 1/3.
Therefore, the solution sets for the given equations are:
1. x = 3/2
2. x = -2, x = -3
3. x = 1/3