Square both sides of the equation. The isolated square root should be easy to square and ,as a reasult, that square root will disappear. But be careful when squaring the other side. It can be easy to square it incorrectly and, if it has square roots, its square roots are not guaranteed to disappear. In short, squaring both sides of an equation will not always eliminate all the square roots!
If there are any square roots remaining, repeat steps 1 through 3.
At this point there should be no square roots left. Based on the type of equation you now have, use appropriate techniques to solve it.
Check your solutions. This is not optional! To get this far both sides of the equation have been squared at least once (at step 2). It is not an error to do this. But squaring both sides of an equation may introduce what are called "extraneous solutions". Extraneous solutions are solutions that fit the squared equation but do not fit the original equation!. Extraneous solutions are not the result of some error. They cannot be avoided by being more careful. So whenever both sides of an equation are squared (or raised to any even power, for that matter), you must check for these extraneous solutions and discard them if you find them.
Let's see this in action:
1. Isolate a square root.
We only have one so there's no choice to be made as to which one to isolate. To isolate our square root all we have to do is subtract 2x from each side:
2. Square both sides.
Squaring the left side is easy. Correctly squaring the right side requires using FOIL on (-2x-7)(-2x-7) or using the . I prefer using the patterns:
which simplifies to:
3. If there are any remaining square roots...
Our square roots are all gone.
4. Use appropriate techniques to solve the equation.
This is a quadratic equation. So we want one side to be zero. Adding 2x and 7 to both sides we get:
Now we factor (or use the Quadratic Formula). This factors without too much difficulty. First the GCF:
then the trinomial factors:
Now we use the Zero Product Property:
2x+7 = 0 or x+4 = 0
Solving these we get:
x = -7/2 or x = -4
5. Check your solution.
Use the original equation to check:
Checking x = -7/2:
Simplifying... Check!
Checking x = -4:
Simplifying... Check!
No extraneous solutions... this time! Don't forget to check for them.
(