Can someone give me directions on how to solve this type of problem. im not sure what to do. (x^2) +6x +10= 2?

Question

All I know is to factor the expression and solve the equation.
first you equal the problem to 0, but what after that?
(x^2) +6x +10= 2
(x^2)+6x+10-2=0

I need to know how the answer
x=-2 and x=-4
i have no idea how you get that answer
what are the steps after you equal it to 0

Answer 1

You need to make the equation fit the form of a Quadratic Equation which has the form ax^2 + bx + c = 0, so your first step above is correct.

You than need to factor the equation. Try to think of 2 numbers which multiply together to give "c" and add together to give "b".

Your equation is
x^2 + 6x + 8 = 0
you can see that 2 x 4 = 8 and 2 + 4 = 6.
You can rewrite your equation as
(x+2)(x+4) = 0

Now you can see that if x = -2 the term x+2 would = 0, and multiplying things by zero give zero as an answer. So, when x = -2 the expression is True and therefore x = -2 is one of the answers to this problem. The same applies if x = -4

So for your expression the answers are:
x = -2 and x = -4

Answer 2

Simplify a little more first: x^2+6x+8
Now we see if the problem is factorable before we result to the tedious work of the quadratic equation (which is: x= (-b plus or minus (the square root of (b^2 - 4ac))) / (2a). with the quadratic equation, if you recall, being ax^2+bx+c).

How do we factor the problem? We know it will be (x + __) (x +__) because it is x^2 and the middle term and last term are both positive then the signs must be positive.

We know that the middle term's coefficient is created by the sum of the factors of the last term. We ask ourselves: what are the factors of 8? 8 and 1. 2 and 4. Will either of those create 6 if we add them together? Yes.

2 +4 =6. Therefore we know that it is (x+2)(x+4)=0
We now put each parentheses equal to 0 because anything multiplied by 0 = 0. x+2=0 and x+4=0. Subtract 2 and 4 and we get x=-2 and x=-4.

Answer 3

first, combine all the like terms... in this one, it's just gonna be the 10 and 2, so you'll have
(x^2) + 6x + 8 = 0

then you use the quadratic formula: x = -b (+or-) the square root of ((b^2) - 4ac) and divide all that by 2a.... plug everything in:

x= -6 (+or-) the square root of (6^2) - 4(1 x 8) then divide by 2(1)

simplify to x = -6 (+or-) square root of 36 - 32 all over 2

the square root of 4 (36-32) is 2 (since 2 x 2 is 4)..... so you have: x = (-6 (+or-) 2)/2.

you're going to have two answers to this equation, because of the + OR -... first do the + ..... x= (- 6 + 2)/2 ... x = - 4 / 2 = -2

then do the - .... x = ( - 6 - 2)/2 ..... x = -8 / 2 = - 4

so your final answer will be x = -2 OR -4

hope this made sense and helped.

Good Luck!

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just looked, and the first answer is another way to do the problem. it just depends on which is easier for you.

Answer 4

there are many ways solving quadratic equation,

the first method is use scientific calculator CASIO fx - 570MS
1. press the MODE button until you see EQN then press number 1
2. press DEGREE? button number 2
3. then key in a? = 1, b = 6, and c = 8
4. finally you press the equal button x = -2 and -4

the second method is use formula to find the value of x

x = [-b +/- sqrt( b^2 - 4ac)] divided by 2a

your equation is x^2 + 6x + 8 = 0
so a = 1, b = 6 and c = 8
x = [-6 +/- sqrt (6^2 - 4(1)(8)] divided by 2(1)
x = [-6 +/- sqrt 4] divided by 2
x = [-6 +/- 2] divided by 2
x = -6 + 2 divided by 2 = -2
and
x = -6 - 2 divided by 2 = -4
therefore x = -2 and -4

the third method is cross factoring
(x + 2)(x + 4) = 0
so, x + 2 = 0
x = -2
and, x + 4 = 0
x = -4

Answer 5

For it to equal zero, one part or the other of a multiplicand should be zero.

x^2 +6x +8 = 0

If we reduce the binomial thus:

(x + 4 )(x + 2) = 0

x + 4 can be zero, in which case x = -4,
or x +2 can be zero, in which case x = -2.

The answer is then two possibilities,

x = -4 and x = -2.

Of course, if you graphed the equation you would see it's a parabola anyway, so that's how there can be two x values for the function of x.

Answer 6

There are several ways to do it. The easiest (and sometimes longest) is to use the quadradic formula. You have to get your equation into standard form, though. Standard form looks like this:
ax^2 + bx + c = 0
The right side of the equation MUST be zero or it won't work.
So, a = whatever number is in front of x^2
b = whatever number is in front of x
c = whatever number doesn't have a variable with it.
Write down what a, b, and c are equal to and substitute (replace) thier values into the following equation:
{-b +/- sqrt (b^2 - 4ac) } divided by 2a
(sqrt means take the square root of everything in the parenthesis)

in your case
a = 1 (if there is no number in front of your variable, then it is understood to be one. It's the only number you can multiply by anything and get that anything right back)
b = 6
c = 8
so................
{-b +/- sqrt (b^2 - 4ac) } divided by 2a
= {-[6] +/- sqrt ([6]^2 - 4[1][8]) } divided by 2[1]
= {-6 +/- sqrt (36 - 32 } divided by 2
= {-6 +/- sqrt (4) } divided by 2
= {-6 +/- 2} divided by 2
So now it's -6 + (2) divided by 2 or -6 - (2) divided by 2
-4 divided by 2 or -8 divided by 2
-2 or -4
Practice a few. You're going to keep seeing these things until you finally graduate college.

Answer 7

so after you do the first step, you simplify and get
(x^2) + 6x +8 = 0. If you don't like factoring, there's also the quadratic formula where a,b,c are the co-effecients of the equation. for example, in this case a = 1; b = 6; c = 8. then you do (-b + ((b^2)-4ac))/2a and (-b - ((b^2)-4ac))/2a.
one is -b plus and the other is -b minus. This will give you your roots as well.

Answer 8

So far, so good.

x^2 + 6x + 8 = 0
This factors nicely into:
(x+4)(x+2) = 0

So you're multiplying two things together and getting zero. The only way that can happen is if one of the two things you're multiplying together is zero.

Hence, the solutions to this problem are x=-4 and x=-2.

Answer 9

quadritic formula gives you
a= 1 b= 6 c= 8
-6 +/- square root of 36-4(8)
-6+2= -4 -6+-2= -8. those would be the x intercepts: -4, -2. line of symetry would be -3. what else do you need to know? what does the question say?

another way of doing that would be to factor. (x+-4)(x+-2)=0.

Answer 10

x^2 + 6x + 8 = 0

(x + 4)(x+2) = 0

x = -4 or x = -2