Question 914191
Let {{{ z = x^2 }}}
{{{ z^2 - 16z - 80 = 0 }}}
complete the square:
{{{ z^2 - 16z + (16/2)^2 = 80 + (16/2)^2 }}}
{{{ z^2 - 16z + 64 = 80 + 64 }}}
{{{ ( z - 8 )^2 = 12^2 }}}
{{{ z - 8 = 12 }}}
{{{ z = 20 }}}
and also:
{{{ z - 8 = -12 }}}
{{{ z = -4 }}}
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{{{ z = x^2 }}}
{{{ 20 = x^2 }}}
{{{ x = 2*sqrt(5) }}}
{{{ x = -2*sqrt(5) }}}
and
{{{ z = x^2 }}}
{{{ -4 = x^2 }}}
{{{ x = 2i }}}
{{{ x = -2i }}}
these are the 4 solutions
You can plug them back in to check
The real solutions are the first 2