2 More quad equations. Just need checking

[npaggs]

Sorry I didn't think to add these two in my other post.
I just want to see if I've made any mistakes here.

Sorry I'm not good with tex coding.

Use Quad Formula:
\(\displaystyle 2=5x^2+4x\)

Put it in General Form

\(\displaystyle 0=5x^2+4x-2\)

Use Quad Formula:

-4 ± sqrt(16+40)
______________
10

Which gets me

-4 ± sqrt(56)
__________
10

-4 ± 3 sqrt(6)
___________
10

Is it good so far?

Next.. Complete the Square
\(\displaystyle 1/2x^2-3x = 2\)

Divide equation by \(\displaystyle 1/2\)

\(\displaystyle x^2 - 6x = 4\)

Divide b by 2 then Square it, and add to both sides

\(\displaystyle x^2 - 6x + 9 = 13\)

Perfect Square..

\(\displaystyle (x-3)^2 = 13\)

Square root both sides

\(\displaystyle x-3 = sqrt 13\)

x = 3± sqrt 13

Is that correct?

Thanks in advance !

 

[Deleted member 4993]

Sorry I didn't think to add these two in my other post.
I just want to see if I've made any mistakes here.

Sorry I'm not good with tex coding.

Use Quad Formula:
\(\displaystyle 2=5x^2+4x\)

Put it in General Form

\(\displaystyle 0=5x^2+4x-2\)

Use Quad Formula:

-4 ± sqrt(16+40)
______________
10

Which gets me

-4 ± sqrt(56)
__________
10

-4 ± 3 sqrt(6)<<<<< sqrt(56)=sqrt(4*14) = 2 * sqrt(14)
___________
10

Is it good so far?

Next.. Complete the Square
\(\displaystyle 1/2x^2-3x = 2\)

Divide equation by \(\displaystyle 1/2\)

\(\displaystyle x^2 - 6x = 4\)

Divide b by 2 then Square it, and add to both sides

\(\displaystyle x^2 - 6x + 9 = 13\)

Perfect Square..

\(\displaystyle (x-3)^2 = 13\)

Square root both sides

\(\displaystyle x-3 = sqrt 13\)

x = 3± sqrt 13<<<< Correct

However, you should check your own answer by putting these values back into the equation and check

1/2 x^2 -3x -2

= 1/2 (3+sqrt(13))^2 - 3*(3+sqrt(13)) - 2

= 1/2[9 + 6*sqrt(13) + 13] - 9 - 3*sqrt(13) - 2

= 11 + 3*sqrt(13) - 3*sqrt(13) - 11

= 0

Most probably correct

Is that correct?

Thanks in advance !

 

[npaggs]

Ah, thank you very much.