Quadratic Equations and tranforming

[Gr8fu13]

The sample problem: 14(x-4)-(x+2)=(x+2)(x-4)
They transformed this into standard form:
x^2 - 15x + 50 = 0

I have no CLUE as to how they got this. My problem I need to transfer into standard form is:
12(x-4)-(x-2)=(x+2)(x-4)

Can someone please point me in the right direction?
Thanks!

 

[galactus]

No Clue?.Really?. All they done was expand both sides and set it all equal to 0.

\(\displaystyle 14(x-4)-(x+2)=13x-58\)

\(\displaystyle (x+2)(x-4)=x^{2}-2x-8\)

\(\displaystyle 13x-58-(x^{2}-2x-8)=-x^{2}+15x-50\)

Which you can rewrite as \(\displaystyle x^{2}-15x+50\) by multiplying by -1.

 

[mmm4444bot]

Simplifying the given equation requires knowing some skills.

You need to know the Distributive Property and how it's used to multiply expressions of the form a(b + c), to get rid of the parentheses.

You need to know how to apply the Distributive Property twice, to multiply expressions of the form (a + b)*(c + d).

One method to apply the Distributive Property twice goes by the acronym "FOIL".

You need to know how to combine what's called "like terms", and how to collect the combined terms to one side of the equation.

Does any of this sound familiar?

If not, please let us know because these message boards are not a good forum to teach basics. We can refer you to online lessons that cover these basics.

Otherwise, please post any attempts to work on this exercise.

Cheers

 

[Gr8fu13]

Thanks so much. I was trying to get everything on one side of the equation and was thinking FOIL method for some reason. Thanks for clearifying that!