How do you solve x-3=sqrt(30- 2x)?

1 Answer
May 12, 2016

x=7

Explanation:

Isolate the square root on the left hand side:
Original: x-3=sqrt (30-2x)
Isolate: -sqrt(30-2x)=x+3
Tidy up:sqrt(30-2x)=x-3

Eliminate the radical on the left hand side:
Raise both sides to the second power sqrt(30-2x)^2=(x-3)^2
30-2x=x^2-6x+9

Solve the quadratic equation:
x^2-4x-21=0
This equation has two rational roots {x1,x2}={7,3}

sqrt(30-2x) = x-3

Plug in the 7 as x
sqrt(30-2)•(7) = (7)-3

Simplify
sqrt16 = 4

x = 7