Question 575948
{{{ a^2-2a-48=0 }}}
{{{ a^2 - 2a = 48 }}}
Complete the square:
Take 1/2 of the coefficient of {{{ x }}},
square it and add it to both sides
{{{ a^2 - 2a + (-2/2)^2  = 48+ (-2/2)^2 }}}
{{{ a^2 - 2a + 1 = 48 + 1 }}}
{{{ ( a - 1 )^2 = 7^2 }}}
Take the square root of both sides
{{{ a - 1 = 7 }}}
{{{ a = 8 }}}
and, also, taking the negative root,
{{{ a - 1 = -7 }}}
{{{ a = -6 }}}
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{{{ a - 8 = 0 }}}
{{{ a + 6 = 0 }}}
{{{ ( a - 8 )*( a + 6 ) = 0 }}}