Question

Considere as expressões: A = 5 (x – 3) – 2x (x – 3) e B = 4 – (3x + 1)2
. Resolva a equação A = B – 18

Answer 1

A = 5 (x – 3) – 2x (x – 3) = 5x-15-2x²+6x = 11x-15-2x²
B = 4 – (3x + 1)2 = 4-6x-2 = 2-6x
.
Resolva a equação A = B – 18

A = B – 18
11x - 15 - 2x² = 2 - 6x - 18
11x - 15 - 2x² - 2 + 6x + 18 = 0
17x +1 -2x² = 0

a=-2, b=17 e c= 1

báskara, temos:

x=-b+-raiz(b²-4ac)/2a
x=-17+-raiz(17²-4*-2*1)/2*-2
x=-17+-raiz(289+8)/-4
x=-14+-raiz(297)/-4
x1= -14+raiz(297)/-4 ---> x1=7/2+raiz (297)
x2= -14-raiz(297)/-4 ---> x2= 7/2-raiz(297)

Answer 2

A = 5 (x – 3) – 2x (x – 3)
A=  5x - 15 - 2x^2 + 6x 
A= - 2x^2 + 11x - 15

B = 4 – (3x + 1)2
B= 4 - (9x^2 + 2.3x.1 + 1)
B= 4 - 9x^2 - 6x - 1
B= - 9x^2 - 6x + 3

A = B – 18

- 2x^2 + 11x - 15 =  - 9x^2 - 6x + 3 - 18
- 2x^2 + 11x - 15 + 9x^2 + 6x - 3 + 18 = 0
 7x^2 + 17x  = 0

x(7x - 17) = 0
    x1 = 0

7x2 - 17 =0
7x2 =  17
x2 = 17
          7