Question

MÉTODO DE COMPLETAR QUADRADOS
$x^2+3x=16$

Answer 1

$x^2+3x=16\\\\x^2+3x+\boxed{~}^2-\boxed{~}^2=16\\\\x^2+2.x. \frac{3}{2} +(\frac{3}{2})^2-( \frac{3}{2} )^2=16\\\\\left ( x+\frac{3}{2} \right)^2-\left ( \frac{3}{2} \right)^2=16\\\\\left ( x+\frac{3}{2} \right)^2- \frac{9}{4} =16\\\\\left ( x+\frac{3}{2} \right)^2=16+ \frac{9}{4} \\\\\left ( x+\frac{3}{2} \right)^2= \frac{73}{4}$

$x+\frac{3}{2}= \pm \sqrt{\frac{73}{4} } \\\\x'= \sqrt{ \frac{73}{4} } ~~- \frac{3}{2} ~~\Rightarrow~~\boxed{x'= \frac{-3+ \sqrt{73} }{2}}\\\\\\x''=- \sqrt{ \frac{73}{4} }~- \frac{3}{2} ~~\Rightarrow~~\boxed{x''=\frac{-3- \sqrt{73} }{2} }$