Question

Equações:
a) x²=x+12
b) 2x²=-5-7x
c) 25x²=20x-4
d) 2x²=-5-7x

Answer 1

a)
x² = x + 12
x² - x - 12 = 0
a = 1; b = - 1; c = - 12

Δ = b² - 4.ac
Δ = (-1)² - 4.1.(-12)
Δ = 1 - 4. (-12) 
Δ = 1 + 48
Δ = 49

x = - b +/- √Δ = - ( - 1) +/- √49
          2a                 2.1

x = 1 + 7 = 8/2 = 4
         2

x = 1 - 7 = - 6/2 = - 3
        2

R.: x = 4 e x = - 3
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b)
2x² = 12x - 18
2x² - 12x + 18 = 0 (:2)

x² - 6x + 9 = 0
a = 1; b = - 6; c = 9

Δ = b² - 4ac
Δ = (-6)² - 4.1.9
Δ = 36 - 36
Δ = 0

x = - b +/-  √Δ
            2a

x = 6 = 3
      2

R.: x = 3
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c)
25x² = 20x - 4
25x² - 20x + 4 = 0 
a = 25; b = - 20; c = 4

Δ = b² - 4ac
Δ = (-20)² - 4.25.4
Δ = 400 - 100.4
Δ = 400 - 400
Δ = 0

x = - b +/- √Δ = - ( - 20) +/- 0
           2a                2.25

x = - b  = - ( - 20)  =  20  (:10)  = 2
      2a         2.25       50  (:10)     5

R.: x = 2/5
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d)
2x² = - 5 - 7x

2x² + 7x + 5 = 0
a = 2; b = 7; c = 5

Δ = b² - 4ac
Δ = 7² - 4.2.5
Δ = 49 - 8.5
Δ = 49 - 40
Δ = 9

x = - b +/- √Δ  = - 7 +/- √9
            2a              2.2

x' = - 7 + 3  = - 4  = - 1
           4         4

x" = - 7 - 3  = - 10 (:2) =  - 5
            4          4  (:2)       2

R.: x = - 1 e x = - 5/2