Question

Aplique o processo de Baskara, resolva as seguintes equações de segundo grau a)x^2-8x+16=49 b)x^2-30x+100=1 c)x^2+6x=-5 d)(x+2).(x -1)+2x=x - 3 e)(2-x)^2+2=2x+1+10​

Answer 1

a) x² - 8x + 16 = 49

x² - 8x + 16 - 49 = 0

x² - 8x - 33 = 0

∆ = (-8)² - 4.1.(-33)

∆ = 64 + 132

∆ = 196

$x = \frac{ - ( -8 ) + - \sqrt{196} }{2 \times 1}$

$x = \frac{8 + - 14}{2}$

$x1 = \frac{8 + 14}{2} = 11 \\ x2 = \frac{8 - 14}{2} = - 3$

b) x² - 30x + 100 = 1

x² - 30x + 100 - 1 = 0

x² - 30x + 99 = 0

∆ = (-30)² - 4.1.99

∆ = 900 - 396

∆ = 504

$x = \frac{ - ( - 30) + - \sqrt{504} }{2 \times 1}$

$x = \frac{30 + - 6 \sqrt{14} }{2}$

$x = \frac{30 + 6 \sqrt{14} }{2} \\ x = \frac{30 - 6 \sqrt{14} }{2}$

$x1 = 15 + 3 \sqrt{14} \\ x2 = 15 - 3 \sqrt{14}$

c) x² + 6x = -5

x² + 6x + 5 = 0

∆ = 6² - 4.1.5

∆ = 36 - 20

∆ = 16

$x = \frac{ - 6 + - \sqrt{16} }{2 \times 1}$

$x = \frac{ - 6 + - 4}{2}$

$x 1= \frac{ - 6 + 4}{2} = - 1 \\ x2 = \frac{ - 6 - 4}{2} = - 5$

d) (x+2) . (x-1) + 2x = x - 3

x² - x + 2x - 2 + 2x = x - 3

x² + 3x - 2 - x + 3 = 0

x² + 2x + 1 = 0

∆ = 2² - 4.1.1

∆ = 4 - 4

∆ = 0

$x = \frac{ - 2 + - \sqrt{0} }{2 \times 1}$

$x = \frac{2 + - 0}{2}$

$x = \frac{ - 2}{2}$

$x = - 1$

e) (2-x)² + 2 = 2x + 1 + 10

4 - 4x + x² + 2 = 2x + 11

6 - 4x + x² = 2x + 11

6 - 4x + x² - 2x - 11 = 0

-5 - 6x + x² = 0

x² - 6x - 5 = 0

∆ = (-6)² - 4.1.(-5)

∆ = 36 + 20

∆ = 56

$x = \frac{ - ( - 6) + - \sqrt{56} }{2 \times 1}$

$x = \frac{6 + - 2 \sqrt{14} }{2}$

$x = \frac{ 6 + 2 \sqrt{14} }{2} \\ x = \frac{6 - 2 \sqrt{14} }{2}$

$x1 = 3 + \sqrt{14} \\ x2 = 3 - \sqrt{14}$