You can put this solution on YOUR website! Since "=" is on the same key as "+", I'm going to assume the equation is actually:
If this wrong, the following procedure should help you solve the correct equation.
Here's a procedure for solving this kind of equation:
Isolate (or "solve for") one of the square roots.
Square both sides of the equation. (Remember, squaring a side of an equation is multiplying it by itself. It is not squaring each individual term.)
If there are still any square roots in the equation, repeat steps 1, 2 and 3.
At this point, there should be NO square roots remaining. Use appropriate techniques to solve the type equation you now have.
Check your answer(s)! This is not optional. Squaring both sides of an equation can introduce what are called extraneous solutions. Extraneous solutions are solutions that work in the squared equation but not in the original equation. Check your answer(s) in the original equation. Any that do not work are extraneous and must be rejected! Notes:
Extraneous solutions are NOT caused by errors. Even expert mathematicians must check their answers on these problems.
If it happens that all your answers are extraneous, it just means that there are no solutions to the equation.
Let's see this in action:
1. Isolate a square root. There is only one so we must isolate it. This square root is not isolated. The 4 needs to go away. Adding 4 to each side we get:
2. Square both sides:
Squaring a square root is easy. But the right side can easily be done incorrectly. is NOT !!! Exponents do not distribute! To square this we must either use FOIL on (x+24)(x+24) or use the pattern with the "a" being x and the "b" being 24. I prefer the pattern:
which simplifies to:
3. There are no square roots remaining so we can proceed to step 4.
4. Solve the equation. This is a quadratic equation so we want one side to be zero. Subtracting 5x from each side we get:
Now we factor or use the Quadratic Formula. This does not factor so we must use the Quadratic Formula:
which simplifies as follows:
With the negative inside the square root it means one of four things. In order from most likely to least likely they are:
My guess at the correct equation was wrong. If this is the case then try following the procedure above on the correct equation.
There are no solutions to the equation (because complex solutions are not allowed).
Complex solutions are allowed. If this is the case then continue to simplify, including the use of "i" to represent .
A mistake was made above. (I do make mistakes and you are welcome to look for them. But I have checked my work and I do not see any errors.)
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