SOLUTION: I meant I need help completing the square 6x^2+5x=6

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Question 412980: I meant I need help completing the square
6x^2+5x=6
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can help
6x%5E2+%2B+5x+=+6
first, divide through by 6, so
x%5E2 has coefficient = 1
x%5E2+%2B+%285%2F6%29%2Ax+=+1
Now take 1/2 of the coefficient of x,
square it, and add it to both sides
+x%5E2+%2B+%285%2F6%29%2Ax+%2B+%285%2F12%29%5E2+=+1++%2B++%285%2F12%29%5E2
x%5E2+%2B++%285%2F6%29%2Ax+%2B+25%2F144+=+144%2F144+%2B+25%2F144
+x%5E2+%2B++%285%2F6%29%2Ax+%2B+25%2F144+=+169%2F144+
Both sides are now a perfect square
+%28x+%2B+5%2F12%29%5E2+=+%2813%2F12%29%5E2
Take the square root of both sides
x+%2B+5%2F12+=+13%2F12
x+=+8%2F12
x+=+2%2F3
And there is also a negative square root
x+%2B+5%2F12+=+-13%2F12
x+=+-3%2F2
The roots are 2/3 and -3/2
I can check this by
%28x+-+2%2F3%29%2A%28x+%2B+3%2F2%29+=+0
x%5E2+-%28+2%2F3%29%2Ax+%2B+%283%2F2%29%2Ax+-+1+=+0
x%5E2+-%284%2F6%29%2Ax+%2B+%289%2F6%29%2Ax+=+1
Multiply through by 6
6x%5E2+-+4x+%2B+9x+=+6
6x%5E2+%2B+5x+=+6
OK