Solve each quadratic equation by completing the square2x^2-4x-3=0

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Solve `2x^2-4x-3=0` by completing the square.

(1) In order to complete the square, the leading coefficient should be 1 so divide both sides by 2:

`x^2-2x-3/2=0`

(2) Now we add a number so that the first three terms form a perfect square trinomial. We take 1/2 of the coefficient of the klinear term and square it.

`x^2-2x+1-1-3/2=0` . To preserve the equality we added a 1 and a -1, effectively adding zero to the left side.

(3) The first three terms form a perfect square trinomial and can be rewritten. We also combine the constant terms:

`(x-1)^2-5/2=0` Then:

`(x-1)^2=5/2`

`sqrt((x-1)^2)=+-sqrt(5/2)`

`x-1=+-sqrt(5/2)` Rationalizing to get rid of the radical in the denominator and adding 1 yields:

`x=1+-(sqrt(10))/2` which is the result.

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