SOLUTION: Please help to solve this equation by completing the square: 3x^2 - x - 1 = 0

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Question 571216: Please help to solve this equation by completing the square:
3x^2 - x - 1 = 0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3x%5E2+-+x+-+1+=+0+
+3x%5E2+-+x+=+1+
+x%5E2+-%281%2F3%29%2Ax+=+1%2F3+
Take 1/2 of the coefficient of x, square it
and add it to both sides
+x%5E2+-%281%2F3%29%2Ax+%2B++%28-1%2F6%29%5E2+=+1%2F3++%2B+%28-1%2F6%29%5E2+
+x%5E2+-%281%2F3%29%2Ax+%2B+1%2F36+=+12%2F36+%2B+1%2F36+
+%28+x+-+1%2F6+%29%5E2+=+13%2F36+
Take the square root of both sides
+x+-+1%2F6+=+sqrt%28+13+%29+%2F+6+
+x+=+%28+1+%2B+sqrt%2813%29+%29+%2F+6+
and, also
+x+=+%28+1+-+sqrt%2813%29+%29+%2F+6+
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check the solutions:


Multiply both sides by +12+
+1+-+2%2Asqrt%2813%29+%2B+13+-+2+%2B+2%2Asqrt%2813%29+-+12+=+0+
+1+%2B+13+-+2+-+12+=+0+
+0+=+0+
OK. You can check other solution