How do you find x for this equation x^+9x+20=6?

Question

Please show steps. Thanks :)

Answer 1

You should equal the equation to 0, so: x^2 + 9x + 14 = 0.

Now, how can you get 14 using multiplication? 1 and 14, 2 and 7. Which one, using either subtraction or addition gets you 9 (because of 9x)? 2 plus 7. So,

(x+ 2)(x + 7) = 0.

Take each parenthesis and equal it to zero, then solve for x.
x + 2 = 0 x + 7 = 0.
- 2 -2 -7 -7

x = -2 or -7.

Check: - 2 times - 2 + 9(-2) + 20 = 6.
4 + -18 + 20 = 6 CORRECT

-7 times -7 + 9(-7) + 20 = 6.
49 - 63 + 20 = 6. CORRECT.

Answer 2

subtract 6 from both sides (you always have to have the equation equal to 0) X^2 +9X+20=6
-6 =-6
X^2+9X+14=0

List all the factors of 14 (20-6) 1 and 14, 2 and 7

Okay you notice that you have 2 signs (+ and +) the second sign (furthest to the right) will always tell you what the signs will be when you factor. If the furthest sign to the right is + that means that both of the signs will be the same (+ and + or - and -). If the furthest sign to the right is a + and the furthest sign to the left is a - then both factored signs will be -. If the furthest sign to the right is a + and the furthest sign to the left is a + then both of the factored signs will be a +. (this is how your problem is.

if the furthest sign to the right is a - that means the sign will be different. (X+ ) (X- ).

Back to your problem. If you read the first paragraph you will see that so far you have (X+ ) (X+ ). The factors of 14 (1 and 14, 2 and 7) have get a 9 in the middle if you were to FOIL (multiply) the two X equations together to check your answer. So you get (X+7) (X+2)=0

Set both equations equal to 0

X+7=0 X+2=0
-7+-7 -2=-2
X=-7 X=-2

So your answer is X= -7 or X= -2

Answer 3

Hi,
x^+9x+20=6?
Since you have a caret sign after the first "x," I'm going to assume that that should be x^2:
x² +9x + 20 =6
x²+9x +20-6 = 0 (Put in standard form by subtracting 6 from each side of the equation.)
x²+9x +20-6 = 0
x²+9x +14 = 0
(x+2)(x+7)= 0 (Find two factors of 14 that add up to 9.)
x+2=0..|x+7 = 0 (In accordance with the zero factor theorem, set
x=-2.....|x=-7........each term equal to zero and solve for x.
{-7,-2}

Hope this is what you had in mind.

FE

Answer 4

x^2+9x+20=6
x^2+9x+14=0
(x+7)(x+2)=0 < Now we know that either x+7=0 or x+2=0
therefore, x=-7 or x=-2. Both solutions work.