Completing squares??

Question

#1
Find c that makes
x^2 - 8x + c
a perfect square trimonial, then write as binomial

#2 solve by completing square
x^2 - 12x + 4=0

#3 complete square
2x^2 + 8x -1=0

Answer 1

Question 1
x² - 8x - 16
(x² - 8x + 16) - 16 - 16
(x - 4)² - 32
x² - 8x + 16 - 32
x² - 8x - 16
c = 16

Question 2
(x² - 12x + 36) - 36 + 4 = 0
(x - 6)² - 32 = 0
(x - 6) = ±√ 32
x - 6 = ± 4√2
x = 6 ± 4√2

Question 3
x² + 4x - 1/2 = 0
(x² + 4x + 4) - 4 - 1/2 = 0
(x + 2)² = 9/2
(x + 2) = ± 3 / √2
(x + 2) = ± (3/2)√2
x = - 2 ± (3/2)√2

Answer 2

#1
c = (-8/2)²
c = 16

x² - 8x + 16
=(x - 4)²

#2
x² - 12x + 4 = 0
x² - 12x + 4 + 32 = 32
(x - 6)² = 32
x-6 = sqrt(32)
x = 6 +/- sqrt(16*2)
x = 6 + 4sqrt(2) ; x = 6 - 4sqrt(2)


#3
2x² + 8x - 1 = 0
x² + 4x - 1/2 = 0
x² + 4x - 1/2 + 9/2 = 9/2
(x + 2)² = 9/2
x + 2 = +/- sqrt(9/2)
x = -2 +/- 3/sqrt(2)
x = -2 + 3/sqrt(2) ; x = -2 - 3/sqrt(2)