Question

qual as raizes da equação 4x – x(x – 2) = 5

Answer 1

$4x-x(x-2)=5\\\\4x-x^2+2x=5\\\\x^2-2x-4x+5=0\\\\x^2-6x+5=0\\\\(x-1)\cdot(x-5)=0\\\\\\\begin{matrix}x'-1=0\\\\\boxed{x'=1}\end{matrix}\qquad\qquad\qquad\qquad\begin{matrix}x''-5=0\\\\\boxed{x''=5}\end{matrix}\\\\\\\\\boxed{\boxed{S=\left\{1,\ 5\right\}}}$

Answer 2

4x - x.(x - 2) = 5
4x - x² + 2x = 5
- x² + 4x + 2x = 5
- x² + 6x - 5 = 0 (-1)
x² - 6x + 5 = 
a = 1; b = - 6; c = 5

Δ = b² - 4ac
Δ = (- 6)² - 4.1.5
Δ = 36 - 20
Δ = 16

x = - b +/- √Δ = - ( - 6) +/- √16
           2a                2.1

x' = 6 + 4 = 10/2 = 5
         2

x" = 6 - 4 = 2/2 = 1
         2

R.: x = 5 e x = 1