SOLUTION: I need to solve by completing the square.I'm not sure how to do 1 half of negative s. The problem is {{{s^2-s-6=0}}}

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Question 167476: I need to solve by completing the square.I'm not sure how to do 1 half of negative s. The problem is s%5E2-s-6=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

s%5E2-s-6 Start with the left side of the equation.


Take half of the s coefficient -1 to get -1%2F2. In other words, %281%2F2%29%28-1%29=-1%2F2.


Now square -1%2F2 to get 1%2F4. In other words, %28-1%2F2%29%5E2=%28-1%2F2%29%28-1%2F2%29=1%2F4


s%5E2-s%2Bhighlight%281%2F4-1%2F4%29-6 Now add and subtract 1%2F4. Make sure to place this after the "s" term. Notice how 1%2F4-1%2F4=0. So the expression is not changed.


%28s%5E2-s%2B1%2F4%29-1%2F4-6 Group the first three terms.


%28s-1%2F2%29%5E2-1%2F4-6 Factor s%5E2-s%2B1%2F4 to get %28s-1%2F2%29%5E2.


%28s-1%2F2%29%5E2-25%2F4 Combine like terms.


So after completing the square, s%5E2-s-6 transforms to %28s-1%2F2%29%5E2-25%2F4. So s%5E2-s-6=%28s-1%2F2%29%5E2-25%2F4.


So s%5E2-s-6=0 is equivalent to %28s-1%2F2%29%5E2-25%2F4=0.

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%28s-1%2F2%29%5E2-25%2F4=0 Start with the completed square set to 0.


%28s-1%2F2%29%5E2=0%2B25%2F4 Add 25%2F4 to both sides.


%28s-1%2F2%29%5E2=25%2F4 Combine like terms.


x-1%2F2=0%2B-sqrt%2825%2F4%29 Take the square root of both sides.


s-1%2F2=sqrt%2825%2F4%29 or s-1%2F2=-sqrt%2825%2F4%29 Break up the "plus/minus" to form two equations.


s-1%2F2=5%2F2 or s-1%2F2=-5%2F2 Take the square root of 25%2F4 to get 5%2F2. Note: %285%2F2%29%5E2=25%2F4 so sqrt%2825%2F4%29=5%2F2


s=1%2F2%2B5%2F2 or s=1%2F2-5%2F2 Add 1%2F2 to both sides.


s=%281%2B5%29%2F2 or s=%281-5%29%2F2 Combine the fractions


s=6%2F2 or s=-4%2F2 Combine the numerators


s=3 or s=-2 Reduce.


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Answer:


So the solutions are s=3 or s=-2.