Solving Equations with One Radical Term
Example
Solve for w:
| Solution |
 |
= w |
| Step 1 Isolate the radical term.
Add 2 to both sides.
|
 |
= 2 + w |
| Step 2 Apply the Principle of Powers.
Square both sides. |
 |
= (2 + w)2 |
| Step 3 Solve the resulting equation.
Write the right side as a product.
FOIL the right side.
Write in standard form.
Factor. Use the Zero Product Property. Solve for w.
Step 4 Check the solution. |
2w2
+ 11w + 14 2w2
+ 11w + 14
w2 + 7w + 10
(w + 2)(w + 5) w + 2 = 0 or w
+ 5 w = -2 or w |
= (2 + w)(2 + w)
= 4 + 4w + w2
= 0
= 0 = 0
= -5 |
Since w = -5 does not check, the only solution is w
= -2.
|