SOLUTION: Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 1 + x + 2x2 = 0

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Question 962474: Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.
1 + x + 2x2 = 0
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
start with 2x^2 + x + 1 = 0

subtract 1 from both sides of the equation to get:

2x^2 + x = -1

factor out a 2 on the left side of the equation to get:

2 * (x^2 + x/2) = -1

complete the squares on x^2 + x/2 to get:

2 * ((x+1/4)^2 - (1/16)) = -1

simplify by distibuting the multiplication to get:

2 * (x+1/4)^2 - 2*(1/16) = -1

simplify further to get:

2 * (x+1/4)^2 - 1/8 = -1

add 1/8 to both sides of the equation to get:

2 * (x + 1/4)^2 = -7/8

divide both sides of the equation by 2 to get:

(x + 1/4)^2 = -7/16 ***** this is your solution.

continue further to solve for x if you care to, but the problem did not require you to do this.

take the square root of both sides of the equation to get:

x + 1/4 = plus or minus sqrt(-7/16)

subtract 1/4 from both sides of the equation to get x = -1/4 plus or minus sqrt(-7/16).

since sqrt(-7/16) is the same as sqrt(7/16) * i, your solution becomes:

x = -1/4 plus or minus sqrt(7/16) * i.

your problem was to convert it to the form of (x + p)2 = q.

the solution to that is:

(x + 1/4)^2 = -7/16

as indicated above with the *****