Question 566510
{{{ (x + 1)(x + 1) + (x + 2)(x + 2) = 5 }}}
{{{ x^2 +2x +1 + x^2 +4x +4 = 5 }}}
{{{ 2x^2 +6x +5 = 5 }}}
Subtract {{{5}}} from both sides
{{{ 2x^2 + 6x = 0 }}}
{{{ x*( 2x + 6 ) = 0 }}}
{{{ x = 0 }}}
{{{ 2x + 6 = 0 }}}
{{{ 2x = -6 }}}
{{{ x = -3 }}}
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check:
{{{ (x + 1)(x + 1) + (x + 2)(x + 2) = 5 }}}
{{{ (-3 + 1)(-3 + 1) + (-3 + 2)(-3 + 2) = 5 }}}
{{{ -2*(-2) + (-1)*(-1) = 5 }}}
{{{ 4 + 1 = 5 }}}
{{{ 5 = 5 }}}
and
{{{ (0 + 1)(0 + 1) + (0 + 2)(0 + 2) = 5 }}}
{{{ 1*1 + 2*2 = 5 }}}
{{{ 1 + 4 = 5 }}}
{{{ 5 = 5 }}}
OK