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

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Answer 1 · 2016-05-12T08:46:29

x=7

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