Question 969850
{{{ x^2  - 6x - 4 = 0 }}}
Add {{{ 4 }}} to both sides
{{{ x^2  - 6x = 4 }}}
Take {{{ 1/2 }}} of the coefficient of The
{{{ x }}} term, square it, and add it to both sides
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{{{ x^2 - 6x + ( -6/2 )^2 = 4 + ( -6/2 )^2 }}}
{{{ x^2 - 6x + 9 = 4 + 9 }}}
{{{ x^2 - 6x + 9 = 13 }}}
{{{ ( x - 3 )^2 = 13 }}}
Take the square root of both sides
{{{ x - 3 = sqrt(13) }}}
{{{ x = 3 + sqrt(13) }}}
And also, taking the negative square root,
{{{ x = 3 - sqrt(13) }}}
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check answer:
{{{ x^2  - 6x - 4 = 0 }}}
{{{ ( 3 - sqrt(13) )^2 - 6*( 3 - sqrt(13) )  - 4 = 0 }}}
{{{ 9 - 6*sqrt(13) + 13 - 18 + 6*sqrt(13) - 4 = 0 }}}
{{{ 9 + 13 - 18 - 4 = 0 }}}
{{{ 22 - 22 = 0 }}}
OK
You can check {{{ x = 3 + sqrt(13) }}}