Step-by-step explanation:
Original equation
x+3 = √3x+37
Isolate
-√3x+37 = -x-3
Tidy up
√3x+37 = x+3
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√3x+37)2 = (x+3)2
After squaring
3x+37 = x2+6x+9
STEP
3
:
Solve the quadratic equation
Rearranged equation
x2 + 3x -28 = 0
This equation has two rational roots:
{x1, x2}={4, -7}
STEP
4
:
Check that the first solution is correct
Original equation, root isolated, after tidy up
√3x+37 = x+3
Plug in 4 for x
√3•(4)+37 = (4)+3
Simplify
√49 = 7
Solution checks !!
Solution is:
x = 4
STEP
5
:
Check that the second solution is correct
Original equation, root isolated, after tidy up
√3x+37 = x+3
Plug in -7 for x
√3•(-7)+37 = (-7)+3
Simplify
√16 = -4
Solution does not check
4 ≠ -4
One solution was found :
x = 4
