SOLUTION: Solve each of the following quadratic equations by completing the square... #22. X^2-6X-3=0 #28. 2X^2+10X+11=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve each of the following quadratic equations by completing the square... #22. X^2-6X-3=0 #28. 2X^2+10X+11=0      Log On


   

Question 85296: Solve each of the following quadratic equations by completing the square...
#22. X^2-6X-3=0
#28. 2X^2+10X+11=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+6x+-3+=+0
First add 3 to both sides
x%5E2+-+6x+=+3
Then take 1/2 of the coefficient of x, square it, add to both sides
%286%2F2%29%5E2+=+9
x%5E2+-+6x+%2B+9+=+3+%2B+9
%28x+-+3%29%5E2+=+12
x+-+3+=+0+%2B+2%2Asqrt%283%29
x+=+3+%2B+2%2Asqrt%283%29 answer
and
%28x+-+3%29%5E2+=+12
x+-+3+=+0+-+2%2Asqrt%283%29
x+=+3+-+2%2Asqrt%283%29 answer
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2x%5E2+%2B+10x+%2B+11+=+0
divided both sides by 2
x%5E2+%2B+5x++%2B+11%2F2+=+0
subtract 11/2 from both sides
x%5E2+%2B+5x+=+-%2811%2F2%29
x%5E2+%2B+5x+%2B+25%2F4+=+25%2F4+-+22%2F4
%28x+%2B+5%2F2%29%5E2+=+3%2F4
x+%2B+5%2F2+=+sqrt%283%29%2F2
x+=+%28-5+%2B+sqrt%283%29%29%2F2 answer
and
x+%2B+5%2F2+=+0+-+sqrt%283%29%2F2
x+=+%28-5+-+sqrt%283%29%29%2F2 answer