Can anyone help me with completing the Square? 5x^2-12x=-2?

Answer 1

5x^2-12x=-2
5x^2-12x+2=0 (add 2)
x^2-12/5x+2/5=0 (take out the 5 )
x^2-12/5x = -2/5 (subtract 2/5)

(x^2-12/5x+?) = -2/5+? (prepare for completing square)
x^2-12/5x+((-12/5)/2)^2 = -2/5+(-12/5)/2)^2 (use (b/2)^2)
x^2-12/5x+36/25 = 26/25 (multiply them out)
(x-6/5)^2= 26/25 (joining factor)
x-6/5= +/- sqr(26)/5 (take a square root)
x= 6/5 +/- sqr(26)/5

Answer 2

First factor out the 5: 5(x^2 - 12/5) = -2

To start the square divide the 12/5 by 2 getting 6/5 then write:

5(x - 6/5)^2.....

Multiplying this out gives 5(x^2 - 12/5x + 36/16)

or 5x^2 - 12x + 11.25. Complete the square by adding an additional 11.25 to the -2 on the other side.

So you have 5(x - 6/5)^2 = 9.25

Finally divide both sides by 5 to get (x - 6/5)^2 = 1.85

Answer 3

5x^2 - 12x = -2
Divide both sides by 5 :
x^2 - (12/5)x = -2/5

Take half the constant of x, and square it.
(1/2) of (12/5) = 6/5.
(6/5)^2 = 36/25

Now add this to both sides of the equation :
x^2 - (12/5)x + 36/25 = -2/5 + 36/25
Factorise :
(x - 6/5)^2 = 26/25
Take the square root of both sides :
x - 6/5 = ± sqrt(26) / 5
Add 6/5 to both sides :
x = [6 ± sqrt(26)] / 5

Answer 4

Completing the square, hmmm?

5x^2 - 12x = -2
5x^2 - 12x + 2 = 0

Using the convention ax^2 + bx + c, we first, get the a to equal 1:

x^2 - 12x/5 + 2/5 = 0
x^2 - 2.4x + 0.4 = 0

Next, for a binomial square, c = (b/2)^2. (Consider some basic binomial squares such as x^2-2x+1 or x^2+4x+4 to see that this is true) 2.4 in half is 1.2; square it's 1.44. 1.44 - 0.4 = 1.04, so we add 1.04 to both sides to make the square on the left.

x^2 - 2.4x + 0.4 + 1.04 = 0 + 1.04
x^2 - 2.4x + 1.44 = 1.04

Now you have your square on the left, so take the square root of both sides:

x^2 - 2.4x + 1.44 = 1.04
(x - 1.2)^2 = 1.04
x - 1.2 = sqrt(1.04) or x - 1.2 = -sqrt(1.04) (remember that a square root can be either positive or negative.)

And finish the solution:
x = 1.2 + sqrt(1.04) or 1.2 - sqrt(1.04)

To check one of the roots,
5x^2 - 12x = -2
5(1.2 + sqrt(1.04))^2 - 12(1.2 + sqrt(1.04)) = -2
5(1.44 + 2.4sqrt(1.04) + 1.04) - 14.4 - 12sqrt(1.04) = -2
7.2 + 12sqrt(1.04) + 5.2 - 14.4 - 12sqrt(1.04) = -2
12.4 - 14.4 = -2
-2 = -2
Checking the other,
5x^2 - 12x = -2
5(1.2 - sqrt(1.04))^2 - 12(1.2 - sqrt(1.04)) = -2
5(1.44 - 2.4sqrt(1.04) + 1.04) - 14.4 + 12sqrt(1.04) = -2
7.2 - 12sqrt(1.04) + 5.2 - 14.4 + 12sqrt(1.04) = -2
12.4 - 14.4 = -2

Yes, we have a winner. Hope that helps.

Answer 5

this equation can be rewritten as shown below:

5x^2 +(-12)x +2 = 0

Now use the quadradic equation to solve for x

x=[-b plus/minus (b^2 - 4ac)^1/2]/2a
a = 5
b = -12
c = 2

two possible answers
1st
x= [-(-12) + (12^2-4(5)(2))^0.5]/2(5)
x = [12 + (144-40)^0.5]/10
x = (12 + 10.19)10
x = 2.219

2nd
x = ((12-10.19)/10
x = 0.181

Check

5(2.219)^2 -12(2.219)+2 = 24.62-26.62+2=0 ok!

you can check the other answer yourself

Answer 6

You have to get rid of the 5 first. Divide the whole thing by 5, and then do completing the square. Then you get x^2 - 2.4x = -.4, when you do (.5b)^2 you get 1.44, so the new equation is x^2 -2.4x + 1.44 = 1.04. This simplifies to (x - 1.2)^2 = 1.04, so, x - 1.2 = + or -sqr(1.04), so the answer is x = 1.2 + sqr(1.04) or x = 1.2 - sqr(1.04).