Question

Determine o valor de x:
a)(5x+12)=67
b)x-59=179
c)(4x-12)=36
d)7x-17=60
e)(2x-6) elevado a 2 potência =64
f)(3x+2) elevado a 2 potência =121

Answer 1

a)
(5x + 12 ) = 67
5x = 67 - 12
5x = 55
x = 55/5
x = 11
****************************
b)
x - 59 = 179
x = 179 + 59
x = 238
*****************************
c)
(4x - 12) = 36
4x = 36 +12
4x = 48
x = 48/4
x = 12
---------------------------------
d)
7x - 17 = 60
7x = 60 + 17
7x = 77
x = 77/7
x = 11
------------------------------------------
e)
(2x - 6)² = 64
4x² - 2.6.2x + 36 = 64
4x² - 24x + 36 - 64 = 0
4x² - 24x - 28 = 0  (:4)
x² - 6x - 7 = 0

a = 1; b = - 6; c = - 7

Δ = b² - 4ac
Δ = (-6)² - 4.1.(-7)
Δ = 36 - 4.(-7)
Δ = 36 + 28
Δ = 64

x = - b +/- √Δ
          2a

x = 6 + 8 = 14/2 = 7
        2

x = 6 - 8 = -2/2 = - 1
         2

R.: x = - 1 e x = 7
_____________________________
f)
(3x + 2)² = 121
9x² + 2.2.3x + 4 = 121
9x² + 12x + 4 - 121 = 0
9x² + 12x - 117 = 0

a = 9; b = 12; c = - 117

Δ = b² - 4ac
Δ = 12² - 4.9.(-117)
Δ = 144 - 36.(- 117)
Δ = 144 + 4212
Δ = 4356
√Δ = 66

x = - b +/- √Δ  = - 12 +/- √4356
          2a                   2.9

x = - 12 + 66  = 54/18 = 3
            18

x = - 12 - 66  = - 78 (:2)  =  - 39
          18           18  (:2)        9

R.: x = 3 e x = - 39/9 
********************************