Question 1058267
{{{ 9x^2 + 6x = 8 }}}
Divide both sides by {{{ 9 }}}
{{{ x^2 + (2/3)*x = 8/9 }}}
Take 1/2 of the coefficient of the {{{x}}}
term, square it, and add it to both sides
{{{ x^2 + (2/3)*x + (1/3)^2 = 8/9 + (1/3)^2 }}}
{{{ x^2 + (2/3)*x + 1/9 = 8/9 + 1/9 }}}
{{{ x^2 + (2/3)*x + 1/9 = 1
{{{ ( x + 1/3 )^2 = 1^2 }}}
Take the square root of both sides
{{{ x + 1/3 = 1 }}}
{{{ x = 2/3 }}}
and, taking the negative square root of {{{ 1^2 }}},
{{{ x + 1/3 = -1 }}}
{{{ x = -4/3 }}}
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check the solutions:
{{{ ( x - 2/3 )*( x + 4/3 )= 0 }}}
{{{ x^2 - (2/3)*x + (4/3)*x - 8/9 = 0 }}}
{{{ x^2 + (2/3)*x - 8/9 = 0 }}}
Multiply both sides by {{{ 9 }}}
{{{ 9x^2 + 6x - 8 = 0 }}}
{{{ 9x^2 + 6x = 8 }}}
OK