Solving Quadratic Equations/Completing the Square?

Question

I need some homework help. I'm supposed to solve the following equations by completing the square and solving for x. A thorough explanation along with the answer would be greatly appreciated. :)

2x^2-24x+2= -62

and

x^2+x+1=7/4

Answer 1

Question 1
x² - 12x + 32 = 0
(x² - 12x + 36) - 36 + 32 = 0
(x - 6)² = 4
x - 6 = ± 2
x = 8 , x = 4

Question 2
4x² + 4x + 4 = 7
4x² + 4x - 3 = 0
4(x² + x - 3/4) = 0
x² + x - 3/4 = 0
(x² + x + 1/4) - 1 = 0
(x + 1/2)² = 1
x + 1/2 = ± 1
x = - 1/2 ± 1
x = 1/2 , x = - 3/2

Answer 2

2x^2 -24x + 2 = -62 , divide by 2

x^2 - 12x + 1 = -31 , subtract one from both sides

x^2 - 12x -32, then complete the square which is
(x^2 + ax) = (x + a/2)^2 - (a/2)^2

(x - 6)^2 - 36 = -32 , add 36 to both sides

(x - 6)^2 = 4 , square root both sides

x - 6 = (+-) 4, add six to both sides

x = 6 (+-) 2

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x^2 + x + 1 = 7/4 , subtract one from both sides

x^2 + x = 3/4 , complete the square

(x + 1/2)^2 - 1/4 = 3/4, add 1/4 to both sides

(x + 1/2)^2 = 1 , square root both sides

x + 1/2 = (+-) 1 , subtract 1/2 from both sides

x = -1/2 (+-) 1

Answer 3

you want to rationalize the denominator x - a million = ± ?(-a million/2) x - a million = ± ?-a million / ?2 x - a million = ± i / ?2 x - a million = ± i?2 / 2 x = a million ± (i?2 / 2) x = (2 ± i?2) / 2 bear in concepts that you'll't have a ? contained in the denominator