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 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 .
