Question

As Raízes da equação x (x+5) = 374 é igual a:

Answer 1

As raízes da equação são: x'= 17 e x"= -22.

Organizando a equação e na sequência aplicando a fórmula de Bháskara, temos:

$x(x+5)=374\\\\\large\boxed{x^2+5x-374=0}$

$\Delta=b^2-4ac\\\\\Delta=5^2-4\cdot1\cdot(-374)\\\\\Delta=25+1496\\\\\Large\boxed{\Delta=1521}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-5\pm\sqrt{1521}}{2\cdot1}\\\\\Large\boxed{x=\dfrac{-5\pm39}{2}}\\\\\\\boxed{\large\begin {array}{l}x'=\dfrac{-5+39}{2}\\\\x'=\dfrac{34}{2}\\\\\Large\boxed{\boxed{x'=17}}\Huge\checkmark\end {array}}\quad\quad\boxed{\large\begin {array}{l}x"=\dfrac{-5-39}{2}\\\\x"=\dfrac{-44}{2}\\\\\Large\boxed{\boxed{x"=-22}}\Huge\checkmark\end {array}}$

Portanto, as raízes são: x'= 17 e x"= -22.

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