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

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) (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 *****

RELATED QUESTIONS
Use the method of completing the square to transform the quadratic equation into the... (answered by josgarithmetic)

Use the technique of completing the square to transform the quadratic equation below into (answered by flame8855)

Use the method of completing the square to solve the equation 3 = 2x2 +... (answered by nerdybill,ewatrrr)

1. Use the discriminant to determine the number of solutions for x^2-3x+6=0 2. Solve... (answered by MathLover1)

Use the method of completing the square to find the standard form of the quadratic... (answered by lwsshak3)

Use the Completing the Square method to find the vertex form of the quadratic function... (answered by Mathtut,nerdybill)

use the method of completing the square to solve for x... (answered by tommyt3rd)

Convert the equation to standard form by completing the square... (answered by MathLover1)