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Algebra/solution of quadratic equation by completing square

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Expert: - 7/15/2010


Question

solution of quadratic
Kindly
solve the quadratic equation by completing square

Answer
Divide both sides by -3 to get a 1 in front of the s².  This gives s² + s/3 - 1/3 = 0.

Divide 1/3 (the factor on s) by 2, giving 1/6, and then square it, giving 1/6²= 1/36.
This gives s² + s/3 +1/36 - 1/36 - 1/3 = 0.

"Combine the 1/36 and the 1/3 by noting that 1/3 is 12/36, to get 13/36,
so we now have  s² + s/3 +1/36   -   13/36 = 0."

Factor the square and move the constant term to the right, giving (s + 1/6)² = 13/36.

Take the squareroot of both sides, given s + 1/6 = ±(√13)/6.

This gives s = (-1 ± √13)/6.
Check this in -3s²-s+1 to make sure you get 0.

Scott A Wilson

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