Completing the square math help please

[AMD Lover]

How do I do this problem by completing the square?

[Hotnuggets]

i do believe you want to get them all on one side and then you can go from there

[Chris is awesome]

10X^2-20X-92 = 0

 

10(X^2-2X)-92 = 0

 

10((X-1)^2-1)-92 = 0

 

10(X-1)^2 - 102 = 0

 

I think.

[Nineshadow]

It's a simple quadratic equation. ()

10x² - 92 = 20x

10x² - 20x - 92 = 0

 

 

Δ = b² - 4ac = 400 - 4*(10 -92) =  400 - 328 = 72 

x₁= (-b + sqrtΔ) / 4 =(20 + 6sqrt2)/4 = (10 + 3sqrt2) / 2

x₂ =(-b - sqrtΔ)/4 = (20 - 6sqrt2)/4 = (10 - 3sqrt2) / 2

Now we know this : ax² +bx + c = a(x - x₁) (x- x₂) = 0

So, a, (x- x1) and (x - x2) must be 0(one at a time).However,we know a can't be 0,because it's 10.So,we have :

x - x1 = 0 (solve this yourself,you know x1)

x - x2 = 0 (solve this yourself, you know x2)

[Nineshadow]

10X^2-20X-92 = 0

 

10(X^2-2X)-92 = 0

 

10((X-1)^2-1)-92 = 0

 

10(X-1)^2 - 102 = 0

 

I think.

You want to re-write the first equation as (a +b)(c +d) = 0,so then you can assume a + b = 0 or c + d =0.

[msevilgenius]

10X^2-20X-92 = 0

 

10(X^2-2X)-92 = 0

 

10((X-1)^2-1)-92 = 0

 

10(X-1)^2 - 102 = 0

 

I think.

Yes I think that's right, just need the last couple of steps:

 

10(X-1)^2 = 102

 

(X-1)^2 = 10.2

 

(X-1) = (10.2)^0.5         (^0.5 is the same as square root)

 

X = 1 ± (10.2)^0.5

 

You want to re-write the first equation as (a + B)(c +d) = 0,so then you can assume a + b = 0 or c + d =0.

That's not completing the square though.

[Chris is awesome]

You want to re-write the first equation as (a + B)(c +d) = 0,so then you can assume a + b = 0 or c + d =0.

If I expand my complete the square version:

10(X-1)^2 - 102 = 0

10(x²-2x + 1) -102 = 0

10x²-20x+10 -102 = 0

10x²-92 = 20x

 

It still is the same equation but written in the completed square form as I was taught it.

 

Yes I think that's right, just need the last couple of steps:

 

10(X-1)^2 = 102

 

(X-1)^2 = 10.2

 

(X-1) = (10.2)^-2         (^-2 is the same as square root)

 

X = 1 ± (10.2)^-2

 

That's not completing the square though.

x^-2 is 1/x² x^0.5 is sqroot

[Nineshadow]

That's not completing the square though.

How not?

(x + a)(x + b) = 0

I know a and b,how can I not find out x?

[msevilgenius]

 

How not?

(x + a)(x +  B) = 0

I know a and b,how can I not find out x?

You can find out x, but the method you have used is not completing the square, it is factorising

 

x^-2 is 1/x² x^0.5 is sqroot

Fixed thanks, my bad.