Why do I suck aT math? Quad equation.?

Question

Work.
3x²-5x-8=0
(x-5/6)²-25/36=8/3
(x-5/6)²=8/3+25/36
...................
96/36+25/36=121/36
right?
If it is possible for me...Then I would do it in a formula, but I have to do the other way cause of my teach.
...............
(x-5/6)²=121/36
x-5/6=+/- 11/6
x=-6/6,16/6
x=-1,6

help, why do I suck at math?
And why must we *2 and square it anyways?
How is this suppose to help us in the real world, everything in quad. equations would always =o, then why would we solve it when we already know the equation ='s "0"?

Answer 1

Okay... I think your teach wants you to solve it putting it into this form:
(x + a# )(x - b#) = 0
Where a# and b# are both factors of 8.
Now in this you can't forget about the coefficent 3so jsut pick one of the x's to put it infront of

(3x + )(x - )

Now you have to think of the factors of 8 that will add up when multipled together (using the foil method = F.irst O.uter I.nner L.ast) ) to gie you a 5. The factors of 8 are 2,4 and 1,8... we stil can't forget about the 3. So b/c it is -5 in the original problem, your biggest factor needs to go with the - sign. Lets first try 2,4

(3x + 2)(x - 4)= 0
3x*2 -12X + 2x - 8 = 0
3x*2 - 8X - 8 = 0 Nope didn't work. What if we tried the 3 on the other x?

(x + 2)(3x - 4)= 0
3x*2 -4X + 8x - 8 = 0 We can already tell it will not work with out going any further b/c comining the -4x + 8x only gives us a 4x so lets try the other set of factorrs 1,8

(3x + 1)(x - 8) = 0
3x*2 - 24x +1x -8 = 0 Nope won't give us a 5X in the middle so lets try moving the 3 b/c the larger factor needs to stay with the minus sign

(x + 1)(3x - 8) =0
3x*2 - 8x + 3x - 8x = 0
3x*2 - 5x - 8x = 0 YES! THat is it!!! Okay now what does this mean? How do we solve it?

If, (x + 1)(3x - 8) =0 Then we know it is solved when any value of X makes the whole equation = to zero. When does this happen?
X + 1 = 0
3X - 8 = 0

so when X = -1, 8/3

HTH!

Answer 2

I answered your other question.

I see you are supposed to practice "completing the square" method. Why do you have to DIVIDE (not multiply as * imply) by 2 and square it because that is what completing the square is all about. Ifyou didn't, you won't be able to bring your final formula to (something squared) = something else.

Don't skip so many steps. Write them down!

Your answer is actually incorrect. Try plugging it into the original formula. It does not work. (that's how you check your answers)

3x²-5x-8=0 original formula
x²-(5/3)x - 8/3 = 0 divide all by 3 to have 1 as coeffecient to x
x²-(5/3)x = 8/3 move 8/3 to right of equal sign
x²-(5/3)x + 25/36 = 8/3 + 25/36 add square of half of second term to BOTH SIDE
x²-(5/3)x + 25/36 = 96/36 + 25/36 common denominator...
(x - 5/6)² = 96/36 + 25/36 you already know this step
(x - 5/6)² = 121/36 simplify the right side
x - 5/6 = +/- 11/6 take square root of both sides

x - 5/6 = 11/6 case where sign is PLUS
x = 11/6 + 5/6
x = 16/6
x = 8/3

x - 5/6 = -11/6 case where sign is MINUS
x = -11/6 + 5/6
x = -6/6
x = -1

You don't suck at math. You are actually doing very well. You only made a very simple mistake on above.

How is it supposed to help you? If you go to any science field like engineering, you will be using it all the time. Yes, you already know it will equal to zero. What you don't know is, what you have to give it (to the variable x) to make it zero. That is what you are trying to figure it out.

By the way, learning math is NOT about getting the right answer. That is what calculator is for. It is all about learning how and why. The only mistake you made was on a simple arithematic. Everything else is right. You actually understand this stuff more than you give yourself credit.

Answer 3

Hi,

Let's start with the last question first. When you solve the equation, you find out what x is, not what the equation is.

I think you're trying to do this equation by completing the square which is useful for very little in the real world (to answer your question) but math teachers like it because it's a neat trick and it helps them feel superior. I ought to know. That sucks that your teacher is making you use that convoluted method because the quadratic equation will always give you the correct answer (provided you put the right numbers in), and factoring is way easier.

Ex1:

3x^2 - 5x - 8 = 0
(3x-8)(x+1) = 0

so either
3x-8 = 0 ------> x= 8/3
or
x+1 = 0 -------> x=-1

to check it we can always use the quadratic formula:

{-(b)+-Sqrt(b^2 - 4ac)}/2a
{-(-5)+-Sqrt((25) - 4(3)(-8)}/2(3)
={(5)+-Sqrt((25) + 96)}/6
={(5)+-Sqrt(121)}/6
={5+-(11)}/6
=16/6 = 8/3
or
= -6/6 = -1

I hope that helps,
Matt

Answer 4

I see you're trying to use completing-the-square, but I don't see how you got your second step. You're right that the first step is to move the -1 over, then get rid of the 3 in front of the 3x^2, to get: 3x^2 - 7x = -1 x^2 - (7/3)x = -1/3 Now you want to take half of 7/3, square it, and add it to both sides. This is (7/6)^2. x^2 - (7/3)x + (7/6)^2 = -1/3 + (7/6)^2 This allows you to factor the left into a perfect square (x - (7/6))^2 = -1/3 + (7/6)^2 Simplify the right side, take the square root of both sides to get rid of the radical, and finally add 7/6 to get x by itself. (x - (7/6))^2 = -1/3 + 49/36 (x - (7/6))^2 = -12/36 + 49/36 (x - (7/6))^2 = 37/36 x - 7/6 = ±√(37/36) x - 7/6 = ±(√37)/6 x = 7/6 ± (√37)/6 x = (7±√37)/6 x = (7+√37)/6, (7-√37)/6 And you're wrong that "people ain't good at math". Some certainly are. It's a learnable skill. If you identify as "somebody who is bad at math", it's up to you if you want to change that, or be that way for the rest of your life.

Answer 5

The only error I see in your work is 16/6 is not 6, but 8/3, or 2 2/3. If you can get from the original equation to x = - 6/6, 16/6, you definitely do NOT "suck" at math. The method you are demonstrating is called "completing the square".

Answer 6

How is this supposed to help in the real world?

Math is all about solving for x, y, and/or z. In other words, it's about finding the unknown via a series of rules. Equations aren't going to do didley squat for you if your goal in life is to become a burger flipper but if you want to make a living doing something that involves making decisions and solving problems, then doing well at math is a good start.

But then again, if one batch of potatoes equals 5 ounces and you have to serve three people 15 oz of fries each, how many batches of potatoes do you have to cook?

Train your brain to solve math problems and you can figure out many more of life's problems.