Question

Resolva a equação do segundo grau ;

4+x(x-4)=x

Answer 1

$4+x(x-4)=x\\\\ 4+x^2-4x=x\\\\ 4+x^2-4x-x=0\\\\ x^2-5x+4=0~~~\Rightarrow~~\left\{\!\begin{array}{l} a=1\\b=-5\\c=4 \end{array} \right.\\\\\\ \Delta=b^2-4ac\\\\ \Delta=(-5)^2-4\cdot 1\cdot 4\\\\ \Delta=25-16\\\\ \Delta=9\\\\\\ x=\dfrac{-b\pm \sqrt{\Delta}}{2a}$

$x=\dfrac{-(-5)\pm \sqrt{9}}{2\cdot 1}\\\\\\ x=\dfrac{5\pm 3}{2}\\\\\\ \begin{array}{rcl} x=\dfrac{5-3}{2}&~\text{ ou }~&x=\dfrac{5+3}{2}\\\\ x=\dfrac{2}{2}&~\text{ ou }~&x=\dfrac{8}{2} \end{array}\\\\\\ ~~~~~~\boxed{\begin{array}{rcl} x=1&~\text{ ou }~&x=4 \end{array}}$


Conjunto solução: $S=\{1,\,4\}.$


Bons estudos! :-)

Answer 2

4+x(x-4)=x

4 + x² - 4x = x

x² - 4x - x + 4 = 0

x² - 5x + 4 = 0

A= 1

B= - 5

C= 4

∆= b² - 4ac

∆= ( - 5)² - 4 • 1 • 4

∆= 25 - 16

∆= 9

x= - b ± √∆ /2a

x= - ( - 5) ± √9 /2 • 1

x= 5 ± 3/2

x'= 5 + 3/2 = 8/2 = 4

x''= 5 - 3/2 = 2/2 = 1

S= ( 1 , 4)