Complete the Square?

Question

Question:
2x^2+10x-4=0




I know that you have to divide all by 2-----making it:

x^2+5x-2=0

then move it over:

x^2+5=2

then:

Add (1/2 coeff of x)^2

which makes it----(1/2(5))^2=25/4^2

but that just can't be right....can you help me out?

ty!!

The question says:

Complete the square on 2x^2+10x-4=0. Show all work below. Do not solve the equation. Just complete the square. write your answer in the form a(x-something)^2= number.

Answer 1

This doesn't come out right. Do you have to use the completing the square method? There are others.

Answer 2

2x^2 + 10x -4 =0
x^2 + 5x -2 = 0
x^2 + 5x = +2

get 1/2 of the second term and then square it. add this to both sides of the equation.
since the second term is 5,
[ (5)(1/2) ]^2 this is what we will add to both sides of the equation.

x^2 +5x + [ 5/2 ]^2 = 2 + [ 5/2 ]^2

now factor the left side of the equation by taking the square roots of the first and third terms. the sign in the middle depends on the sign of the 2nd term.

square root of the first term x^2 is x
square root of the third term [ 5/2 ]^2 is [ 5/2 ]
sign of the second term is +

(x + 5/2)(x + 5/2) = 2 + 25/4
(x + 5/2)^2 = (8 + 25)/4
(x + 5/2) = +/- square root of (33/4)
x = - 5/2 +/- square root of (33/4)

you know what to do next

Answer 3

Well, you've got most of it. First you get it to x2 + 5x = 2. But then you take the coefficient of x, which is five, and divide it by two and square it. Add this to both sides. So (5/2)^2 is 25/4. You get x^2 + 5x + 25/4 = 33/4, and if you need to you make it (x + 5/2)^2 = 33/4

Answer 4

Are you sure you have the equation right? From the answer form you have given you should get something like this:

2(x+2)^2=0
2(x^2+4x+4)=0
2x^2+8x+8=0

This is not the right answer, but with the numbers you have given, the equation will not giving integers for the answer. You can't have a square when the last number is negative, unless you are getting into imaginary numbers like 2i.

Answer 5

You were close.

2(X^2+5x-2)=0

2(x^2+2*5x/2-2)=0

2(x^2+ 2*5x/2+25/4-25/4-2)=0

2[(x+5/2)^2 -25/4 -2]=0

2[(x+5/2)^2 +(-2 - 25/4)]=0

2[(x+5/2)^2+(-33/4)]=0

2[(x+5/2)^2-33/4]=0 /dividing by 2 both sides

(x+5/2)^2 - 33/4 = 0

(x+5/2)^2 = 33/4

x+5/2 = +-sqrt(33)/2

x= -5/2 + - sqrt(33)/2

I am slightly drunk ath the moment, but that seems to be the right answer anyway. LOL.Hope that helps.

Answer 6

x^2 + 5x - 2 = 0
x^2 + 5x = 2
x^2 +5x + 6.25 = 2 + 6.25 (half of 5 squared, add to both side)
x^2 + 5x + 6.25 = 8.25
(x + 2.5)^2 = 8.25 (factor the one side)
x + 2.5 = sqrt(8.25) (solve for x)
x = - 2.5 + sqrt(8.25) (square roots have 2 values +/-)
x = 0.372 and -5.372

Answer 7

"Hopeful Poster" is right. Use her answer