Question

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

Answer 1

Answer:

(x + 1/4)^2 = -15/16

Step-by-step explanation:

Answer 2

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 .