Download Steps for Solving an Irrational Equation

Steps for Solving an Irrational Equation
1.
2.
3.
4.
5.
Isolate the most complicated radical expression
Square both sides and simplify
Repeat steps 2 and 3 if there was more than one radical expression
Solve for x
Check for extraneous solutions
Example #1
(
Check for extraneous solutions
3 x + 1 = −4
)
3x + 1 = (− 4)
3x + 1 = 16
3x = 15
x=5
2
3(5) + 1 = −4
2
16 = −4
4 ≠ −4
The equation has no solution because x = 5 is extraneous.
Example #2
Check for extraneous solutions
3x + 7 − x + 2 = 1
(
3x + 7 = 1 + x + 2
3x + 7
) = (1 +
2
x+2
)
2
3x + 7 = 1 + 2 x + 2 + x + 2
2x + 4 = 2 x + 2
(2 x + 4)
2
(
= 2 x+2
)
2
3(− 2) + 7 − − 2 + 2 = 1
1− 0 =1
1=1
and
4 x + 16 x + 16 = 4( x + 2)
3(− 1) + 7 − − 1 + 2 = 1
4 x 2 + 12 x + 8 = 0
4( x + 1)( x + 2 ) = 0
x = −2,−1
4 − 1 =1
2
2 −1 = 1
1=1
The equation has two solutions, x = -2 and x = -1.