SOLUTION: {{{sqrt(6x+7)-sqrt(3x+3)=1}}}

Question 742097:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

Having 2 square roots in an equation, make it a little more complicated to solve than an equation with just one square root.
As for the simpler equations with square roots, you would square both sides of an equal sign; find solutions to the new equation, and then check those solutions against the original equation.
However, the arithmetic is usually easier if you start with one square root on each side of the equal sign, so the recommended first step (before the squaring) is
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FINDING POSSIBLE SOLUTIONS:
Then, we square both sides to get
and simplify to
At this point we can square again and keep chugging along, to get to the solutions.
Alternatively, if we define the equation above can be written as
--> -->
with solutions and , which mean
--> --> --> and
--> --> -->
Any way we get to them, our possible solutions are and .

CHECKING:
makes the original equation true:
,
so is a solution.
also makes the original equation true:
,
so is also a solution.
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