2x^2+3x+1=0?

Question

The answer is -1 and .5 according to the txt.

its the steps that i cant get.

Answer 1

DON'T BOTHER WITH ANYTHING WRITTEN ABOVE. It is all overly confusing. This is the correct way, for your purposes.

2x^2 + 3x + 1 = 0

The easiest way is to factor this equation. So let's try it. Put two pairs of parentheses, with blanks in them.
( )X( )
The purpose of factoring is to simplify a quadratic equation into two simple parenthetical parts. We know there must be pluses, as everything in the equation is positive.
( + )X( + )
Now, to fill the blanks. The last two must be 1, as only 1 X 1 yields 1. The first must be 2x, and first of the second parentheses must be x, as only 2x X x yields 2x^2.
(2x + 1) X (x + 1) = 0
Now, we just need to solve this. As it is multiplication, the only way to make the equation equal 0 is to make one of the pairs of parentheses, or both, equal 0.
If x = -1, then (x + 1) = 0, and 0 X (2(-1) + 1) = 0, as anything times 0 is 0. So one solution is -1.
If x = -0.5, 2(-0.5) + 1) = 0, and (x + (-0.5)) is 0 as well, for the same reason.

Therefore, the two solutions are,
x = -1
x = -0.5 (can also be written as -1/2, obviously)

Factoring was definitely the easiest way to solve this.

I wish you all the best.

Answer 2

Here are the steps:
2x^2 + 3x + 1 = 0
Break the middle term in such a way that its multiplication is equal to product of first and last terms i.e equal to 2x^2 and addition is equal to the middle term itself (ofcourse) i.e equal to 3x
2x^2 + [2x+x] + 1 = 0,

Now group the terms to take the common out
[2x^2 + 2x] + [x+1] = 0,
Take the common element out.
2x[x+1] + 1[x+1] = 0,
Again take out the common elements and you will get the following
[x+1] [2x + 1] = 0,

Now, if the product of two numbers is zero, then atleast one number HAS to be zero. Further if you equate x+1 = 0, you get x = -1. If you equate 2x+1 = 0, you get x = -0.5. So x can have two values in the equation. The answer is following:

So, either x = -1 or x = -0.5

Answer 3

2x^2+3x+1=0

1.) take the first base (2) and find it's factors: 1,2 are the only ones.
2.) take the factors, and put them like this: (2)(1)
3.)because x is squared, it's factors are x and x.
4.) take those x's, and put one with each of the other factors:(2x)(1x)
5.) now, take the factors of the third base (1).
6.) the only factors of 1 are 1 and 1. They can either both be positive or both be negative.(-1x-1=1)(1x1=1)
7.) now, take (2x)(1x). Because the first sign is a (+) in the equation, that means that both are positive. so, (2x+1)(1x+1)=0
now, set each set of parenthesies equal to 0.
2x+1=0
2x= -1
x= -.5


1x+1=0
1x= -1
x= -1
So you're text is actually wrong. the answers are -1 and -.5

Answer 4

2x^2+3x+1=0
(2x+1) (x+1) =0
either part can be 0, so
x= -.5 or x= -1

Answer 5

All algebraic equations that have solutions can be evaluated by constructing a graph of them. The answer is the value where the graph crosses the x axis. This simple quadratic, whose graph is a parabola with two crossings, can be solved by factoring and use of the quadratic equation, but if you work in engineering, physics, operations research, problems are not as simple as this so you need to learn to graph a solution which will find the answer, if it exists, every time.

Answer 6

once you finished the sq., take each and every of the variable words and use them to make a appropriate sq. polynomial. all of us be conscious of that: (a + b)² = a² + 2ab + b² So we could desire to apply what we are given to make that type. 2x² - 3x + a million = 0 <-- first, pass the consistent term to the different component 2x² - 3x + a million - a million = 0 -a million <-- simplify 2x² - 3x = -a million <-- the 1st term must be a appropriate sq.. enable's mult. via 2 2(2x² - 3x) = -a million(2) <-- distribute 4x² - 6x = -2 <-- now we are able to finished the sq.. call this Eq. a million, and set aside. {eq. a million} 4x² - 6x = -2 precise we've our "a²" term, and our "2ab" term. a² = 4x² 2ab = -6x If we take the sq. root of "a²", we are going to discover "a" a = 2x <-- fee for a If we divide 2ab via a, we get 2b. If we set that up, we are able to clean up for b 2ab / a = 2b<-- substitute -6x / 2x = 2b <-- cancel the x -6 / 2 = 2b <-- divide -3 = 2b <-- divide the two facets via 2 -3/2 = b <-- fee for b we've our fee for b. If we sq. it, we've b² (-3/2)² = b² <-- sq. right and backside 9/4 = b² bypass lower back to Equation a million. {eq. a million} 4x² - 6x = -2 remember we already have a² and 2ab. we could desire to function b² into it. What we do to a minimum of one component, we could desire to do to the different. 4x² - 6x + b² = -2 + b² <-- we extra b² to the two facets. Now substitute. 4x² - 6x + 9/4 = -2 + 9/4 <-- discover liquid crystal reveal on precise component 4x² - 6x + 9/4 = -8/4 + 9/4 <-- combine precise component 4x² - 6x + 9/4 = a million/4 <-- now, ingredient left component - remember it somewhat is a appropriate sq. (2x - 3/2)² = a million/4 <-- take the sq. root of the two facets. Use the two helpful and unfavourable values. 2x - 3/2 = +/- ?(a million/4) <-- evaluate radical 2x - 3/2 = +/- a million/2 <-- clean up for x. start up via getting constants to precise 2x - 3/2 + 3/2 = 3/2 +/- a million/2 <-- simplify 2x = 3/2 +/- a million/2 <-- divide via 2 2x/2 = (3/2)/2 +/- (a million/2)/2 <-- cancel left, multiply denominators, precise x = 3/4 +/- a million/4 <-- chop up the +/- into 2 equations x = 3/4 + a million/4 || x = 3/4 - a million/4 <-- clean up x = a million || x = 2/4 = a million/2 <-- solutions So, the suggestions are x = a million, x = a million/2

Answer 7

Use the quadratic formula: -b +/- sqrt(b^2-4ac)/2a
where a=2, b=3, and c=1

or factor to get (2x+1)(x+1)=0
either 2x+1=0 ---->2x=1----->x=.5
or x+1=0------>x= -1

Answer 8

use the quadratic formula
to get the values for x, use the following formula
(-b + (b^2-4ac)^(1/2))/2a and (-b - (b^2-4ac)^(1/2))/2a

remember ax^2 + bx + c = 0

Answer 9

It's in quadratic form, so use the quadratic equation. (It's too hard for me to write the square roots and other symbols, so I'd recomend looking up the formula on wikipedia under quadratic equation.)

Answer 10

x = -0.5

Text is wrong. Try it out...

2(-0.5)^2+3(-0.5)+1=0