Question 1009738
You're not doing the algebra right. Completing
the square should work, though.
{{{ x^2 - x - 12 = 0 }}}
{{{ x^2 - x =12 }}}
{{{ x^2 - x + (-1/2)^2 = 12 + (-1/2)^2 }}}
{{{ x^2 - x + 1/4 = 12 + 1/4 }}}
{{{ x^2 - x + 1/4 = 49/4 }}}
{{{ ( x - 1/2 )^2 = (7/2)^2 }}}
Take the square root of both sides
(1) {{{ x - 1/2 = 7/2 }}}
and, also:
(2) {{{ x - 1/2 = -7/2 }}}
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(1) {{{ x = 8/2 }}}
(1) {{{ x = 4 }}}
and
(2) {{{ x = -6/2 }}}
(2) {{{ x = -3 }}}
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So, the factors are:
{{{ ( x - 4 )*( x + 3 ) = 0 }}}
You could also use the quadratic formula