7. Solve for x and check
This will not factor, so the simplest method for solving is to use
the quadratic formula
Substitute these numbers into the formula.
Do the arithmetic under the radical: first the power, then the
When we finish the arithmetic under the radical, we may as
well remove the parentheses outside the radical.
The checks to these equations are extremely fascinating. Let us
first check the solution
Copy down the original equation
except that wherever you see an x, copy down the solution in
This gives us an extensive order of operations problem. Since
the expressions inside the parentheses are as simplified as possible,
we do the powers first. There is a square in the first term. Note that
the factor being squared is a fraction with a binomial on the top.
When we square the top and square the bottom, we use the
technique for squaring binomials.
This gives us
When we cancel the 3 and the 26, the first fraction has a
denominator of 12, so we would need to multiply the top and bottom
of the second fraction by 2 to get common denominators.
We could easily turn the 5 into a 60/12 to get it over a
common denominator as well, but one finds that when one does
these checks that if we simplify the fractions we already have at this
point, it will make our lives simpler. Note how the radical terms
vanish leaving us with
The fraction simplifies to
The check of
is entirely similar and is left to the reader.
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