Question 1086031
{{{ x^2 - x - 1 = 0 }}}
{{{ ( x + a )^2 = b }}}
{{{ x^2 + 2a*x + a^2 - b = 0 }}}
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Comparing this with the original equation:
{{{ 2a = -1 }}}
{{{ a = -1/2 }}}
and
{{{ a^2 - b = -1 }}}
{{{ (-1/2)^2 - b = -1 }}}
{{{ 1/4 - b = -1 }}}
{{{ b = 1 - 5/4 }}}
{{{ b = 5/4 }}}
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check:
{{{ ( x -1/2 )^2 = 5/4 }}}
{{{ x^2 - x + 1/4 = 5/4 }}}
{{{ x^2 - x - 1 = 0 }}}