Resolva as seguintes equações, usando o completamente de quadrados
A) x²+10x-11= 0
B) 4t²+20t+25= 0
C) 4x²+12x-7= 0
D) 9x²+24x+14= 0
E) n² + 16n - 720 = 0
F) 4x²+9x+2 = 0
G) x² + x -2 = 0
Respostas
Resolva as seguintes equações, usando o completamente de quadrados
A) x²+10x-11= 0
x² = x.x
- 11 = -1(11)
10x = 11 - 1
x² + 10x - 11 = 0
(x - 1)(x + 11) = 0
assim
(x - 1) = 0
x - 1 = 0
x = + 1
e
(x + 11) = 0
x + 11 = 0
x = - 11
B)
4t²+20t+25= 0
4t² = 2t.2t
25 = 5.5
20 = 10 + 10
4t² + 20t + 25 =
(2t + 5)(2t + 5) = 0
assim
(2t + 5) = 0
2t + 5 = 0
2t = - 5
t = - 5/2
x' e x'' = -5/2
C) 4x²+12x-7= 0
4x² = 2x.2x
12 = 14 - 2
-7 = -1(7)
4x² + 12x - 7 =
(2x - 1)(2x + 7) = 0
assim
(2x - 1) = 0
2x - 1 = 0
2x = + 1
x = 1/2
e
(2x + 7) = 0
2x + 7 = 0
2x = - 7
x = - 7/2
D)
9x²+24x+14= 0 ?????????????????????
9x² = 3x.3x
E)
n² + 16n - 720 = 0
n² = n.n
- 720 = -20(36)
16n = 36 - 20
n² + 16n - 720 = 0
(n - 20)(n + 36) = 0
(n - 20) = 0
n - 20 = 0
n = + 20
e
(n + 36) = 0
n + 36 = 0
n = - 36
F) 4x²+9x+2 = 0
4x² = 4x.x
9 = 8 + 1
2 = 1(2)
4x² + 9x + 1 = 0
(4x + 1)(x + 2) = 0
(4x + 1) = 0
4x + 1 = 0
4x = - 1
x = - 1/4
e
(x + 2) = 0
x + 2 = 0
x = - 2
G) x² + x -2 = 0
x² = x.x
1 = 2 - 1
-2 = -1(2)
x² + x - 2 = 0
(x - 1)(x + 2)
(x - 1) = 0
x - 1 = 0
x = + 1
e
(x + 2) = 0
x + 2 = 0
x = - 2