Answer:
The solution to the equation is x=3.
Explanation:
Write the equation:
√(2x+3)=x
Square both sides to get rid of the radical sign:
(√(2x+3))^2=(x)^2
2x+3=x^2
Subtract 2x from both sides:
2x-2x+3=x^2-2x
3=x^2-2x
Subtract 3 from both sides:
3-3=x^2-2x-3
0=x^2-2x+3
x^2-2x-3=0
Solve using the Quadratic Formula:
x=(-b±√(b^2-4ac))/2a
Plug values in for a, b, and c: (a=1, b=-2, c=-3)
x=(-(-2)±√((-2)^2-4×1(-3) ))/(2×1)
Solve:
x=(2±√(4-4(-3) ))/(2×1)
x=(2±√16)/(2×1)
x=(2±4)/(2×1)
x=(2±4)/2
x=(2+4)/2
x=6/2
x=3
x=(2-4)/2
x=-2/2
x=-1
So, the POSSIBLE solutions are x=3 and x=-1. Now, find the real solution, or value, of x.
Plug 3 back into the equation as x:
√(2x+3)=x
√(2(3)+3)=3
√(6+3)=3
√9=3
3=3 ✔
Plug –1 back into the equation as x:
√(2x+3)=x
√(2(-1)+3)=-1
√(-2+3)=-1
√1=-1
1≠-1 ❌
So, the REAL solution to √(2x+3)=x is x = 3.
Hope that helps! Have an amazing rest of your day! :)