Math Question?

Question

Problem
A rectangular garden is 6 meters longer than the width . if the area is to be 135 m2 , find the length and width .

Solution given :

X = width
X = 6=length

A= L x W

Solve : X2 +6x=135
X2 + 6X+9=135 +9
(x + 3) 2=144
X+3 = + or- 144 squared
X +3= + or - 12
X = 9 or X = -15

Where does the 9 in step 6come from ?

Answer 1

Let L be length
Let W be width
L = W + 6
W = W
A = L x W

So...

135 = (W+6) x W

solve
135 = W^2 + 6W
W^2 + 6W - 135 = 0, factoring this....
(W - 9) (W + 15) = 0

W - 9 = 0
or
W + 15 = 0

So...
W = 9 or -15

since a L or W can't be a negative #, the solution is 9. Also, there are 2 solutions (9 and -15) because the equation is of degree 2 (W^2). If you had an equation with a cubed term (W^3) there would be 3 solutions...and so on.

I'm guessing the method the solution used to factor was completing the square.

Answer 2

You want to add 9 so that you can complete the square. you cannot do X^2+6X-135 to complete the square. If you add 9, the equation will become (X+3)^2 = 12^2, now, you can get rid of square and the equation becomes X+3 = + or - 12. If X=12-3=9 or X= -12-3= -15

Answer 3

L=6+W (length is 6 greater than width)

A=L*W=135m^2 (area is length times width)

135=(6+W)*W
135=W^2+6*W
W^2+6*W-135=0

Use the quadratic equation to solve this to be:
(W+15)*(W-9)=0

Therefore, W = -15 or 9 ... to make that statement equal to 0.

In your solution... X^2 + 6*X + 9 = 135 + 9 ...
The 9 is called "completing the square" ... it is added to both sides so that the left side is equal to (X+3)^2 and thus makes solution easier. Simply search online for completing the square to get a full explanation of it.

Answer 4

That nine comes from the fact that x+3=±12. This gives two solutions: one where x+3=12 and another where x+3=-12. The solution x=9 comes from the solution x+3=12

Answer 5

It's from completing the square. x2 + 6x can't be broken down, but x2 + 6x + 9 is of the form x2 + 2nx + n2, where n is some integer. The 9 came from dividing the 6 by 2 then squaring it.

Answer 6

hey,
when x+3 = + or - 12,
we consider two possibilities.
if x+3 = 12
then,
x = 12 - 3
hence,
x = 9.

this is where the 9 comes from.

the next posibility is
x+3 = -12
then
x = -12-3
x=-15.
that explains -15 too.

Answer 7

x + 3 = + of - 12
x = -3 + 12 = 9
x = -3 -12 = -15

Answer 8

Whatever you do to one side, you have to do to the other. The solver chose to add 9 to the right side so that it was a number that cold be squared. But in order to do that, he/she had to add it to the left side as well.

Answer 9

do your own
home work why ask every one else ? what do you learn???????????? nothing