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Answer 1

The radical equation is the last equation. All of the other problems are not radical equations because they don't have radical solutions.

1.) √17x−3=19
Add 3 to both sides.
√17x−3+3=19+3
√17x=22
Solve Square Root.
√17x=22
17x=222 (Square both sides)
17x=484
17x/17 = 484/17
(Divide both sides by 17)
x=484/17

2.) √17−3=19x
Flip the equation.
19x=1.12
Divide both sides by 19.
19x/19=1.12/19
x=0.06

3.) √17−3x=19
Simplifies to:
−3x+4.123106=19
Subtract 4.123106 from both sides.
−3x+4.123106−4.123106=19−4.123106
−3x=14.876894
Divide both sides by -3.
−3x/−3=14.876894/−3
x=−4.958965

4.) √17x−3x=19
Add 3x to both sides.
√17x−3x+3x=19+3x
√17x=3x+19
Solve Square Root.
√17x=3x+19
17x=(3x+19)^2 (Square both sides)
17x=9x^2+114x+361
17x−(9x2+114x+361)=9x^2+114x+361−(9x^2+114x+361) (Subtract 9x^2+114x+361 from both sides)
−9x2−97x−361=0
x=−b±√b2−4ac/2a (Use quadratic formula with a=-9, b=-97, c=-361)
x=−(−97)±√(−97)2−4(−9)(−361) / 2(−9)
x=97±√−3587 / −18