Square both sides of the equation (remembering that exponents do not distribute).
If there is still a square root, repeat steps #1 and #2.
Solve the equation (which should not have any square roots remaining).
Check your answer(s)! This is not just a good idea. It is important. At step #2 we squared both sides of an equation. Squaring both sides of an equation is not wrong. But it can introduce what are called extraneous solutions. Extraneous solutions are solutions which fit the squared equation but do not fit the original (pre-squared) equation. We must check for these extraneous solutions and reject them.
Let's see how this works on your equation.
1. Isolate a square root.
I'll subtract the second square root from each side:
The square root on the left is isolated.
2. Square both sides:
The left side, since it is a single term, is simple to square. On the right side, with two terms, we must use FOIL or the pattern :
which simplifies to:
or
3. If there is still a square root repeat steps #1 and #2. We still have s square root so...
Isolate a square root. There is only one square root so that's the one we need to isolate. Subtracting y and 56 from each side:
Divide both sides by -14:
Square both sides:
16 = y + 7
There are no more square roots so we can move to step 4.
4. Solve.
Subtract 7 from each side:
x = 9
5. Check the solution(s).
Always use the original equation to check.
Checking x = 9: Check!
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