SOLUTION: Can you please show me how to work this quadratic equation by completing the square a^2 - 4a + 5 = 0

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Question 169989: Can you please show me how to work this quadratic equation by completing the square
a^2 - 4a + 5 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

a%5E2-4a%2B5 Start with the left side of the equation.


Take half of the a coefficient -4 to get -2. In other words, %281%2F2%29%28-4%29=-2.


Now square -2 to get 4. In other words, %28-2%29%5E2=%28-2%29%28-2%29=4


a%5E2-4a%2Bhighlight%284-4%29%2B5 Now add and subtract 4. Make sure to place this after the "a" term. Notice how 4-4=0. So the expression is not changed.


%28a%5E2-4a%2B4%29-4%2B5 Group the first three terms.


%28a-2%29%5E2-4%2B5 Factor a%5E2-4a%2B4 to get %28a-2%29%5E2.


%28a-2%29%5E2%2B1 Combine like terms.


So after completing the square, a%5E2-4a%2B5 transforms to %28a-2%29%5E2%2B1. So a%5E2-4a%2B5=%28a-2%29%5E2%2B1.


So a%5E2-4a%2B5=0 is equivalent to %28a-2%29%5E2%2B1=0.


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%28a-2%29%5E2%2B1=0 Start with the given equation.


%28a-2%29%5E2=0-1Subtract 1 from both sides.


%28a-2%29%5E2=-1 Combine like terms.


x-2=0%2B-sqrt%28-1%29 Take the square root of both sides.


a-2=sqrt%28-1%29 or a-2=-sqrt%28-1%29 Break up the "plus/minus" to form two equations.


a-2=i or a-2=-i Replace sqrt%28-1%29 with "i". Remember, i=sqrt%28-1%29


a=2%2Bi or a=2-i Add 2 to both sides.


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Answer:


So the solutions are a=2%2Bi or a=2-i.