Question

Solve the radical equation: √(2x+3)=x (will medal)
The choices are:
x=3 and x=-1
x=3
x=-1
No Solution

I worked it out and at the end of the quadratic equation, I got (x^2)-2x-3=0, with (x-3)(x+1)
I don't understand how they got the positive and negative signs the other way around in the choices. I know the answer is x=3, but I think I just made a small mistake somewhere?

Answer 1

x^2 - 2x - 3 = 0
(x-3)(x+1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1

But we have to test each solution with the original problem to make sure they are valid solutions. Put x = 3 in the original equation:
√(2x+3)=x
x = 3
√(6+3)=3
3 = 3

√(2x+3)=x
x = -1
√(-2+3)=-1
1 is not equal to -1
So x = -1 is extraneous solution.

x = 3

Answer 2

Ohh ok, I forgot to do that step in the beginning that switched the signs around. Thanks @aum

Answer 3

You are welcome.

If (x+a) is a factor then x = -a is a root / zero / solution.
If (x-a) is a factor then x = a is a root / zero / solution.