Question 516139
{{{ x^2 - 4x + 2 = 0 }}}
{{{ x^2 - 4x = -2 }}}
You can complete the square.
Take 1/2 of the coefficient of {{{x}}},
square it , and add it to both sides
{{{ x^2 - 4x + (-4/2)^2 = -2 + (-4/2)^2 }}}
{{{ x^2 - 4x + 4 = -2 + 4 }}}
{{{ ( x - 2)^2 = 2 }}}
Take the square root of both sides
{{{ x - 2 = sqrt(2) }}}
and also
{{{ x - 2 = -sqrt(2) }}}
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So, the roots are:
{{{ x = 2 + sqrt(2) }}}
{{{ x = 2 - sqrt(2) }}}