Beginning and Intermediate Algebra - Wallace Math Courses ...

Example 448.
x =0 or 4 Our Solution
√ √
3x + 9 − x + 4 = − 1 Even index! We will have to check answers
√ √
√
+ x +4 + x + 4 Isolate the first root by adding x + 4
√ √
3x + 9 = x +4 − 1 Square both sides
√
( 3x + 9)
2 √
=( x + 4 − 1) 2 Evaluate exponents
√
3x + 9=x+4−2 x +4 + 1 Combine like terms
√
3x +9=x+5−2 x + 4 Isolate the term with radical
−x − 5 −x − 5 Subtractxand5from both sides
√
2x +4=−2 x + 4 Square both sides
(2x + 4) 2 √
=(−2 x +4)
2 Evaluate exponents
4x 2 + 16x + 16 =4(x + 4) Distribute
4x 2 + 16x + 16 =4x + 16 Make equation equal zero
�
3(0)+9
�
3( − 3) +9
√
− 9+9
− 4x − 16 − 4x − 16 Subtract4x and 16 from both sides
4x 2 + 12x = 0 Factor
4x(x + 3)=0 Set each factor equal to zero
4x = 0 or x +3=0 Solve
4 4 − 3 − 3
x =0 or x = − 3 Check solutions in original
�
− (0)+4 = − 1 Checkx=0first
√ √
9 − 4 = − 1 Take roots
�
− ( − 3)+4
3 − 2=−1 Subtract
1=−1 False, extraneous solution
= − 1 Checkx=−3
�
− ( − 3)+4 = − 1 Add
√ √
0 − 1 = − 1 Take roots
0 − 1=−1 Subtract
− 1=−1 True! It works
x = − 3 Our Solution
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