MAT117Week7DQ2 - x+1=sqrt(2) x=sqrt(2)-1 These would be...

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MAT/117 Week 7 Discussion Question 2 A way to solve quadratic equations is by completing the square in which one takes an equation that does not quite conclude into a squared linear factor, like: x^2+2x=1 First makes it look like a perfect square on one side by adding an appropriate constant to both sides (in this case add 1 to both sides): x^2+2x+1=2 This equation is then factored: (x+1)^2=2 The solutions are found by taking the square root of both sides:
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Unformatted text preview: x+1=sqrt(2) x=sqrt(2)-1 These would be hard to find by just guessing. Also, note that there is a +/- symbol, showing that there are two roots, one using the + sign and the other using the sign. This is usual for quadratics. A quadratic is also known as a second-degree polynomial, it can have at most two distinct roots (which do not have to be real numbers)....
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