Question

A) x(x-5)=-6
B) (x-2) (x-3)=12

Answer 1

X(X-5)=-6

2X-5X=-6

-3X=-6 (-1)

3X=6

X=6÷3

X=2

Answer 2

Resposta:

A) x(x-5) = -6

x² - 5x + 6 = 0

$delta=b^{2} -4.a.c\\ \\ delta=(-5)^{2} -4.1.6\\ \\ delta=25-24\\ \\ delta=1\\ \\ x=\frac{-b+-\sqrt{delta} }{2.a} \\ \\ x=\frac{5+-\sqrt{1} }{2.1} \\ \\ x=\frac{5+-1}{2} \\ \\ x'=\frac{5+1}{2} =\frac{6}{2} =3\\ \\ x''=\frac{5-1}{2} =\frac{4}{2} =2\\ \\ S~(2;~~3)$

B) (x-2)(x-3)=12

x² - 3x - 2x + 6 - 12 = 0

x² - 5x - 6 = 0

$delta=b^{2} -4.a.c\\ \\ delta=(-5)^{2} -4.1.(-6)\\ \\ delta=25+24\\ \\ delta=49\\ \\ x=\frac{-b+-\sqrt{delta} }{2.a} \\ \\ x=\frac{5+-\sqrt{49} }{2} \\ \\ x=\frac{5+-7}{2} \\ \\ x'=\frac{5+7}{2} =\frac{12}{2} =6\\ \\ x''=\frac{5-7}{2} =-\frac{2}{2} =-1\\ \\ S~(6;~~-1)$