Vamos là.
a) x² + 5x + 6 = 0
x² + 5x = -6
x² + 5x + 25/4 = -6 + 25/4
(x - 5/2)² = 1/4
x1 - 5/2 = 1/2 , x2 - 5/2 = -1/2
x1 = 6/2 = 3 , x2 = 4/2 = 2
b) x² + 5x + 4 = 0
x² + 5x = -4
x² + 5x + 25/4 = -4 + 25/4
(x + 5/2)² = 9/4
x1 + 5/2 = 3/2, x2 + 5/2 = -3/2
x1 = -2/2 = -1 , x2 = -8/2 = -4
c) -x² - x + 30 = 0
x² + x = 30
x² + x + 1/4 = 30 + 1/4
(x + 1/2)² = 121/4
x1 + 1/2 = 11/2, x2 + 1/2 = -11/2
x1 = 10/2 = 5 , x2 = -12/2 = -6
d) x² - 3x + 10 = 0
delta negativo, não há raiz real.
e) 7x² + x + 2 = 0
delta negativo, não há raiz real.
f) 6x² + x - 1 = 0
(2x + 1)*(3x - 1) = 0
x1 = -1/2, x2 = 1/3
g) x² - 7x + 12 = 0
x² - 7x = -12
x² - 7x + 49/4 = -12 + 49/4
(x - 7/2)² = 1/4
x1 - 7/2 = 1/2, x2 - 7/2 = -1/2
x2 = 8/2 = 4, x2 = 6/2 = 3
h) x² - 18x + 45 = 0
x² - 18x = -45
x² - 18x + 81 = -45 + 81
(x - 9)² = 36
x1 - 9 = 6 , x2 - 9 = -6
x1 = 15, x2 = 3
i) x² - 6x + 9 = 0
(x - 3)² = 0
x = 3
f) 5x² + 6x + 3 = 0
delta negativo, não há raiz real.
g) 2x² + 5x - 3 = 0
x² + 5x/2 = 3/2
x² + 5x/2 + 25/16 = 3/2 + 25/16
(x + 5/4)² = 49/16
x1 + 5/4 = 7/4, x2 + 5/4 = -7/4
x1 = 2/4 = 1/2, x2 = -12/4 = -3
h) x² - 2x + 1 = 0
(x - 1)² = 0
x = 1
