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=1, b=-10, and c=23
Negate -10 to get 10
Square -10 to get 100 (note: remember when you square -10, 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 1 to get 2
So now the expression breaks down into two parts
or
Now break up the fraction
or
Simplify
or
So the solutions are:
or
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