Question 519838: please help me solve 5k^2+3k-2=0 by completing the square
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! 5k^2 +3k -2 = 0 can be factored, so you do not need to complete the square.
(5k-2)(k+1) = 0
so
k = -1 or 2/5
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Check using FOIL
5k^2 +5k -2k -2 = 5k^2 +3k -2 = 0
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Of course you can complete the square
5k^2 +3k -2 = 0
Add 2 to both sides
5k^2 +3k = 2
Divide through by coefficient of the squared term
k^2 + 3/5k = 2/5
Take 1/2 of the coefficient of the 'k' term, square it and add to the left and right sides.
1/2*3/5 = 3/10
(3/10)^2 = 9/100
k^2 + 3/5k + 9/100 = 2/5 + 9/100
(k + 3/10)^2 = 2/5 + 9/100
k + 3/10 = sqrt(2/5 + 9/100)
k + 3/10 = sqrt(40/100 + 9/100)
k + 3/10 = sqrt(49/100)
k + 3/10 = +or- 7/10
so
k = 7/10 -3/10 = 4/10 = 2/5
or
k = -7/10 -3/10 = -10/10 = -1
.
Same answer, either way.
.
Done.
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