Question

Por favor ayuda !
Completando el cuadrado transforma cada una de las siguientes ecuaciones a la forma : a(x+h)^2=k
a) 2x^2 +3x+1=0
b) 9x^2-30x+25=0
c) 2x^2+5x+1=0
d) 2x^2-4x+10=0

Answer 1

a) 2x² + 3x + 1 = 0
x² + (3/2)x + (1/2) = 0
x² + (3/2)x = (-1/2)
x² + (3/2)x + (3/4)² = (-1/2) + (3/4)²
( x + 3/4 )² = (1/16)
---> (x+3/4)² = (1/4)²

b) 9x² - 30x + 25 = 0
x² - (30/9)x + (25/9) = 0
x² - (10/3)x = (-25/9)
x² - (10/3)x + (5/3)² = (-25/9) + (5/3)²
----> (x - 5/3)² = 0

c) 2x² + 5x + 1 = 0
x² + (5/2)x + (1/2) = 0
x² + (5/2)x = -1/2
x² + (5/2)x + (5/4)² = (-1/2) + (5/4)²
----> (x + 5/4)² = 17/16

d) 2x² - 4x + 10 = 0
x² - 2x + 5 = 0
x² - 2x = -5
x² - 2x + 1 = -5 + 1
----> (x - 1)² = -4