Completing the square:Help???

Question

(1/2)x^2+2x+1=0
I can not figure this out, can you show me step by step!!?

Answer 1

i suggest you clear the fraction first by multiplying both sides by 2 to get:

x^2 + 4x + 2 = 0

then add and subtract half of 4 squared, which happens to be 4, to the left side to get:

x^2 + 4x + 4 + 2 -4 = 0

the first three terms factor as (x+2)^2, to get

(x+2)^2 +2-4 = 0, or

(x+2)^2 -2 = 0, or

(x+2)^2 = 2. This means that x+2 equals + or - square root of 2, giving us:

x+2 = +sqrt(2) or x+2 = -sqrt(2)

So the two solutions are -2 +/- sqrt(2)

Answer 2

Hello

We need a 1 for the leading coefficient so we multiply by 2 giving us

x^2 + 4x +2 = 0 now put the 2 on the right

x^2 + 4x = -2

Taking 1/2 of b(which 4) and square it giving us 4 so we add 4 to both sides and have

x^2 + 4x + 4 = 2

Factoring we have
(x + 2) ^2 = 2 taking the square root of both sides gives us

x + 2 = +/- sqrt(2) so

x = -2 +/- sqrt(2)

Hope This Helps!!

Answer 3

First, multiply it all by 2 to get rid of the fraction:

(1/2)x^2+2x+1=0
x^2 + 4x + 2 = 0

Then, take the coefficient of middle term, 4x, which is 4. Divide it by 2 and square the answer. This is what we need to complete the square.

(4/2)^2 = 4


Now back to the problem:

x^2 + 4x + 2 = 0
(x^2 + 4x +4) + 2 - 4 = 0
(x + 2)^2 = 2
x + 2 = +/- sqrt(2)
x = -2 +/- sqrt(2)

Answer 4

(1/2)x^2 + 2x + 1 = 0

subtract 1 for both sides
(1/2)x^2 + 2x = -1

before completing the square, you need to make sure the leading coefficient is 1. Multiply both sides by 2
x^2 + 4x = -2

add (b/2)^2 for both sides
x^2 + 4x + (4/2)^2 = -2 + (4/2)^2

x^2 + 4x + 2^2 = -2 + 2^2

x^2 + 4x + 4 = -2 + 4

x^2 + 4x + 4 = 2

factor
(x + 2)^2 = 2

take a square root for both sides
x + 2 = +/-√2

subtract 2 for both sides
x = -2 +/- √2

hope this helps

Answer 5

1) Divide everything by 1/2 (or multiply by 2)
2) That will yield x^2 +4x +2 = 0
3) subtract 2 to the both sides, yielding x^2 +4x = -2
4) To complete the square, add HALF of 4, (which is 2) and Square it, which is adding 4 to both sides
5) x^2 +4x + 4 = -2 + 4
6) (x+2)^2 = 2

Answer 6

1/2x^2 + 2x + 1

= 1/2 (x^2 + 4x) + 1
= 1/2 (x^2 + 4x + 4)-4+1
= 1/2 (x+2)^2 - 3

Answer 7

(1/2)x^2+2x+1=0
Multiply by 2:
x^2+4x+2=0
x^2+4x+4-2=0
(x+2)^2=2;
x+2=sqrt(2) and x+2=-sqrt(2);
x=-2+sqrt(2) and x=-2-sqrt(2);
These are the two roots of this equation

Answer 8

x^2 + 4x + 2 = 0
x^2 + 4x + 4 = 2
(x+2)^2=2;
x+2=sqrt(2) and x+2=-sqrt(2)
x=-2+sqrt(2) and x=-2-sqrt(2)

Answer 9

x^2 + 4x + 2 = 0
x^2 + 4x + 4 = 2
(x+2)^2=2;
x+2=sqrt(2) and x+2=-sqrt(2)
x=-2+sqrt(2) and x=-2-sqrt(2)