Question 419891
{{{ x^2 - 4x - 21 = 0 }}}
{{{x^2 - 4x = 21 }}}
Take 1/2 of the coefficient of x, square it,
then add it to both sides
{{{x^2 - 4x + (4/2)^2 = 21 + (4/2)^2 }}}
{{{ x^2 - 4x + 4 = 21 + 4 }}}
Now both sides are perfect squares
{{{ (x - 2)^2 = 5^2 }}}
Take the square root of both sides
{{{ x - 2 = 5}}}
{{{ x = 7 }}}
also,
{{{ x - 2 = -5 }}}
{{{x = -3 }}}
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so, {{{x - 7 = 0}}} and {{{x + 3 = 0 }}} and
{{{ x^2 - 4x - 21 = (x - 7)*(x + 3) }}}