SOLUTION: Solve the equation. Show your work. the following are under one square root symbol: (x=2)(x-6). Not under the sqrt symbolis: =x-5.

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Question 333116: Solve the equation. Show your work.
the following are under one square root symbol: (x=2)(x-6). Not under the sqrt symbolis: =x-5.
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
I assume the equation is:

To solve an equation with square roots:
  1. Isolate a square root
  2. Square both sides of the equation
  3. If there are still any square roots remaining, repeat steps 1 & 2
  4. Solve the equation (now that there are no longer any square roots).
  5. Check your answers! This is more than just a good idea when solving these equations. Whenever you square both sides of an equation (like you did at least once in step 2) you may introduce extraneous solutions. Extraneous solutions are solutions which work in the squared equation but do not work in the original equation. So you have to check you answers, in the original equation, and reject any that do not work.

Let's see how this works:
1) Isolate the square root. Your square root is aleady all by itself on one side of the equation.
2) Square both sides:

Be careful when squaring the right side. Exponents do not distribute! . Use FOIL or a factoring pattern to square it properly.

3) Repeat steps 1 & 2 if there are still any square roots. Your square root is gone so we can proceed.
4) Solve the resulting equation. First we will simplify the left side:

At first this looks like a quadratic equation. But if we subtract from each side, the squared terms disappear:

This is now a simple equation. We'll get the x terms on one side by adding 10x to each side:

Next we'll add 12 to each side:

Then we divide both sides by 6:

5) Check the solution (in the original equation):






Check!
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