Question 1088722
{{{ x^2 + 2x = 17 }}}
Take 1/2 of the x term, square it,
and add it to both sides
{{{ x^2 + 2x + (2/2)^2 = 17 + (2/2)^2 }}}
{{{ x^2 + 2x + 1 = 18 }}}
{{{ ( x + 1 )^2 = ( sqrt(18) )^2 }}}
{{{ x + 1 = sqrt(18) }}}
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{{{ x = 3*sqrt(2) - 1 }}}
and, taking the negative square root:
{{{ x = -3*sqrt(2)  - 1 }}}
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check:
{{{ x^2 + 2x = 17 }}}
{{{ ( 3*sqrt(2) - 1 )^2 + 2*( 3*sqrt(2) - 1 ) = 17 }}}
{{{ 18 - 6*sqrt(2) + 1 + 6*sqrt(2) - 2 = 17 }}}
{{{ 18 - 2 + 1 = 17 }}}
{{{ 17 = 17 }}}
OK
You can check the other solution