How do i solve this quadratic equation?

Question

Can you give me step by step instructions, please?

3x^2+17x-28.9207=0

Answer 1

NOTE: typing this out got a little confusing so +- is clearly (plus or minus) and sqrt means square root of the following quantity. I typed them out as fractions so the long dotted lines, resemble a fraction.


First, know your formula...

X= [-b+.- sqrt(b^2-4ac)
-----------------------------------------
2a


EQUATION: 3x^2+17x-28.9207=0

PLUG INTO FORMULA (STEP ONE)
x= [-17 +- sqrt(17^2 - 4(3)(28.9207)]
------------------------------------------------------
2(3)


STEP TWO
x= -17 +- sqrt (289- 12(28.9207)
----------------------------------------------
6

STEP THREE
x= =17 +- sqrt (289 - -347.0484)
---------------------------------------------------
6

STEP FOUR
x=-17 +- sqrt (-58.0489)
------------------------------------
6

Because therte is no real square root of a negative number, you know it is an "imaginary number" replaced by variable "i"

therefore the answer would be...

17 + - i
--------------
6

also written as...

17 + i
-----------
6

and

17-i
----------
6

Answer 2

Take a look at the problem, I don't know about you, but I couldn't even begin to factor this polynomial into:

(mX+b)(nX+c)

It's just way too complicated. The last number is the telltale number here. No one could expect you to factor 28.9207 in your head.

Instead, you want to use the quadratic formula. It's a plug and chug formula. It's hard to write in text notation, so just google "Quadratic Formula" and take the wikipedia article.

You get two equations from the + or - part of the equation:
one from the '+'
one from the '-'

The result of the '+' equation gives you one root.
The result of the '-' equation gives you the other.

Answer 3

The quadratic formula is:

X= (-b +/- square root(b^2-4*a*c))/2a

in English:

X is equal to negative b plus or minus the square root of b squared minus four times a times c all over two times a; when a quadratic equation is:

AX^2 +BX +C.

So, for your problem:

3x^2 + 17x -28.9207, the equation is:

X= -17 +/- square root ((17*17)-4*3*-28.9207)/2(3)

X=-17 +/- square root ((289)-12*28.9207)/6

X=-17+/- square root (289+347.0484)/6

X=-17 +/- square root (636.0484)/6

X= -17 +/- (25.2219824756)/6

X= (-17 + 25.2219824756)/2

X=8.2219824756/6

X=1.3703304126

OR

X=(-17 - 25.2219824756)/6

X= -42.2219824756/6

X= -7.03699707926

Therefore, the answer to your problem is either:

1.3703304126

OR

-7.03699707926

Answer 4

use the quadratic formula:

(-b+- (sqrt(b^2 - 4ac)))/ 2a

your quadratic equation is in form:

ax^2 + bx + c = 0

Answer 5

x = -17+/- sqrt(17^2-4(3)(-28.9207))/2(3)
=-17+sqrt(289+347.0484)/6
=(-17+25.22)/6
=1.37
AND
=(-17-25.22)/6
=-7.0366666666666


CHECK YOUR WORK! :)
3(1.37)^2+17(1.37)-28.9207=0
5.6307+23.29-28.9207=0

3(-7.03666)^2+17(-7.036666)-28.9207=0
148.544033333333-119.623333333333-28.9207=0

Answer 6

use the quadratic eqaution.

http://en.wikipedia.org/wiki/Quadratic_equation

Answer 7

Ummm....hehe...ummm.....3?!?

Answer 8

Very carefully!!!

Answer 9

x= 1.171805882