How do you find the solution to the quadratic equation $2x^2 - 2x = 1$ ?

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Answer 1 · 2015-05-28T20:20:18

Here's how you solve it by completing the square:

$1 = 2x^2-2x = 2(x^2-x) = 2(x^2 -x +1/4 - 1/4)$

$= 2((x-1/2)^2-1/4)$

Divide both ends by $2$ to get

$(x-1/2)^2-1/4 = 1/2$

Add $1/4$ to both sides to get:

$(x-1/2)^2 = 3/4$

Take the square root of both sides, allowing for both positive and negative possibilities:

$x-1/2 = +-sqrt(3/4) = +-sqrt(3)/sqrt(4) = +-sqrt(3)/2$

Add $1/2$ to both sides to get:

$x = 1/2+- sqrt(3)/2$

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