Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve ( notice , , and )
Plug in a=4, b=-21, and c=27
Negate -21 to get 21
Square -21 to get 441 (note: remember when you square -21, you must square the negative as well. This is because .)
Multiply to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
Multiply 2 and 4 to get 8
So now the expression breaks down into two parts
or
Lets look at the first part:
Add the terms in the numerator
Divide
So one answer is
Now lets look at the second part:
Subtract the terms in the numerator
Divide
So another answer is
So our solutions are:
or
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