Question 579742
{{{ x^2+3x+2=0 }}}
{{{ x^2 + 3x = -2 }}}
Complete the square:
Take 1/2 of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ x^2 + 3x + (3/2)^2 = -2 + (3/2)^2 }}}
{{{ x^2 + 3x + 9/4 = -(8/4) + 9/4 }}}
{{{ ( x + 3/2 )^2 = (1/2)^2 }}}
Take the square root of both sides
{{{ x + 3/2 = 1/2 }}}
{{{ x = -(3/2) + 1/2 }}}
(1) {{{ x = -1 }}} ( one root of the equation )
and, taking the negative square root,
{{{ x + 3/2 = -(1/2) }}}
{{{ x = -(3/2) - 1/2 }}}
(2) {{{ x = -2 }}} ( the other root of th equation )
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Rewriting (1) and (2),
(1) {{{ x + 1 = 0 }}}
(2) {{{ x + 2 = 0 }}}
and
{{{ ( x + 1 )*( x + 2 ) = x^2 + 3x + 2 }}}