SOLUTION: Find the exact and approximate solutions to {{{x^2-5*x+3=0}}}

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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=-5, and c=3



Negate -5 to get 5



Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because .)



Multiply to get



Combine like terms in the radicand (everything under the square root)




Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or



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So the exact solutions are


or



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When you use a calculator, you will find that the approximate solutions are


or