complete the square for xsquared +x+1=0?

Question

how do u find the solution? u have 2 divide the second term (x) by 2 and then square it?

Answer 1

x^2+x+1=0
x^2+2(1/2)x+1=0
X^2+2(1/2)x+(1/2)^2+1-(1/2)^2=0
(x+1/2)^2+3/4=0
(x+1/2)^2=-3/4
x=-1/2+/-√(3/4) i=-1/2+/-√3 * i/2

Answer 2

You have : x^2 + x + 1 = 0

Here's how the rule works.

Take the first two terms, x^2 + x.
(Notice that x is multiplied by 1.)

We have to make this into a square, say (x + A)^2.
Expanding this gives : x^2 + 2Ax + A^2.
(Notice that x is multiplied by 2A.)

Equating these two constants, we get : 2A = 1, or A = 1/2.
And so, A^2 = 1/4.

Now the square looks like this : (x + 1/2)^2.
Expanding gives : x^2 + x + 1/4.

Now you see where the 1/4 came from.
As you correctly stated, you divide the second
term's constant by 2 and then square it,
then add this result to the first two terms.

But because you added the 1/4, to complete the
square, you must also subtract it, on the same side
of the equation, or the equation will not be true.

It can then be combined with the existing constant.

So we end up with :
(x^2 + x + 1/4) + (1 - 1/4) = 0

or, (x + 1/2)^2 + 3/4 = 0

Subtracting 3/4 from both sides gives :
(x + 1/2)^2 = -3/4

Taking the square root of both sides gives :
x + 1/2 = ± sqrt(-3)/2 = ± [sqrt(3)/2] * i

Subtracting 1/2 from both sides gives :
x = -1/2 ± [sqrt(3)/2] * i
as the two complex conjugate solutions.

Answer 3

The general formula for completing the square when the equation is in ax^2+bx+c=0 form is (x+b/(2*a))^2 but we also need to subtract the extra term that comes from this so we subtract (b/(2*a)).

a, b and c are all just numbers that would appear before the x terms.

Answer 4

(a+b)^2 = a^2 + 2ab + b^2

Therefore, assuming a^2=x^2, and 2ab = x, we can see that 2b=1, and b=1/2 --> b^2=1/4
(x+1/2)^2 + ¾ = 0
(x+1/2)^2 = - ¾
Which is not possible because the square of any number is always positive.

Answer 5

x^2+2(x)(1/2)+(1/2)^2+3/4
(x+1/2)^2+[(rt3)/2]^2

Answer 6

this question does not have any roots which means that there is no answer

Answer 7

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