Solve equation for x: y = (-x^2 + 12*x -14) / 3?

Question

Solve equation for x: y = (-x^2 + 12*x -14) / 3
This is part of a more complicated problem and I can't remember how to do this...thanks.

Answer 1

y = (-x^2 + 12x - 14) / 3

The only way to solve this equation for x is to complete the square.

First, multiply 3 both sides,

3y = -x^2 + 12x - 14

Now, multiply both sides by -1. The reason why we want to do this is that we *want* the coefficient of x^2 positive.

-3y = x^2 - 12x + 14

Now, complete the square for the x terms.

-3y = x^2 - 12x + 36 + 14 - 36

{Note how I added and subtracted 36}

Now, factor the now-square trinomial.

-3y = (x - 6)^2 + 14 - 36

Simplify 14 - 36

-3y = (x - 6)^2 - 22

Move the -22 to the left hand side.

22 - 3y = (x - 6)^2

Now, take the square root of both sides. In an equation, whenever you take the square root of both sides, you have to include a "plus or minus" on one of the sides, which I'll denote as "+/-".

+/- (22 - 3y) = x - 6

Moving 6 to the left hand side, we have
6 +/- (22 - 3y) = x

So we have *TWO* solutions for x.

x = 6 + 22 - 3y, x = 6 - (22 - 3y)

We can simplify each one, to

x = 28 - 3y, x = -16 + 3y

So our solution for x are:

x = {28 - 3y, -16 + 3y}

Answer 2

x^2-12x+(14+3y) = 0

x
= (1/2)(12±√[12^2-4(14+3y)])
= 6±√(22-3y)

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Puggy,
You can use quadratic formula to get the answer.

Answer 3

No clue! haha!

I would do
PEMDAS
Parentheses
Exponets
Multiplication
Division
Additon
Subtraction

Maybe that would help! Plus its easier to do it on a piece of paper!