x2+6x+9=36 the frist x is squared

Question

x2 the x is squared i know the answer is 3,-9 Can you help me under stand how to write it out thank you. solve by taking the square roots. thank you

Answer 1

Hi Roseland;

x²+6x+9=36

x²+6x+9 can be factored as (x+3)²=(x+3)(x+3)...

Let's FOIL this...

FIRST...(x)(x)=x²

OUTER...(x)(3)=3x

INNER...(3)(x)=3x

LAST...(3)(3)=9

x²+3x+3x+9

x²+6x+9

(x+3)²=36

Let's take the square root of both sides...

√[(x+3)²=√36

+/-(x+3)=6

Please remember that if you square a number you produce the same result as its negative counterpart squared.

x+3=6, x=3

-(x+3)=6, -x-3=6, -x=9, x=-9

Answer 2

x² +6x +9 =36 is the same as: x²+6x-27 =0 (subtract 36 from both sides)

 

the easiest way to do this is by completing the square, which looks like:

 

(x + ____)(x+_____)

 

to fill in the blanks, you need to find the right numbers.  The correct numbers will be 2 numbers that when multiplied together equal your constant term(-27) and when added together give you 6(the number in front of your x term)

 

so, let's try some:

 

numbers that equal -27 when multiplied:

 

1x-27

27x-1

3x-9

9x-3

 

Al of these terms give you -27 when multiplied together.  TO figure out which pair of numbers is correct, you have to see which 2 will equal 6 when ADDED together:

 

1 and -27 = -26

27 and -1= +26

3 and -9 = -6

9 and -3 = +6

Answer 3

First, make the equation = 0 by subtracting 36 from both sides.

 

x^2 + 6x + 9 - 36 = 0

x^2 + 6x - 27 = 0

 

Then you need to know that you want to end up with a format of (x plus/minus a number)(x plus/minus a number) and this assumes that you know how to solve this kind of equation with the FOIL method. 
If not, that requires another question and answer!

 

You need to be quick with times tables and be able to recognize what numbers, when multiplied, will give you 27, but when added or subtracted from each other, will give you 6. When you play around with it, you figure out that 9 * 3 = 27 and 9 - 3 = 6

 

Then you plug it in so that it makes sense (which ones are subtracted from which)

 

(x + 9)(x - 3) = 0

 

From here, you know that if one of the sets in parentheses equals 0, then the whole thing will equal 0, and therefore your two solutions are x = -9 and x = 3