Help on this math problem please

Solve, try factoring first...

#1. x^2 +3x + 2 = 4


#2. Also if you feel like answering this one

--The length of a rectagnle is 5 ft greater than the width. The of the rectangle is 14ft

What is the Length :
What is the Width:

Thanks Guys!!

1: Make the equation =0 by subtracting 4 on each side:
x^2+3x-2=0

use the equation:

-b+\-root(b^2-4ac)
-------------------------
2a

-3+\-root(9+8)
-------------------
2

There are 2 answers:

-3+root(17)
--------------- = 0.562
2

-3-root(17)
-------------- = -3.562
2

x=0.562 and -3.562


#2: The area of the rectangle is 14ft, so the length is 7 and the width is 2. You can work that out from observation.

1 Firstly move the 4 over from the right hand side to give you:

x^2 + 3x - 2 = 0

Now as this wont obviously factorise you need to use the quadratic equation:

x = [-b +or- sqrt(b^2 -4ac)] /2a where ax^2 +bx +c=0

x= [-3 +or- sqrt(3^2 - (-8))] /2 ---------> = [-3 +or- sqrt (17)]/2

These are your two answers


#2 Start by letting the width equal (x). You can then say the length is equal to (x+5)

I presume you mean the area is 14ft. Well length multiplied by width = area, therefore:

x(x+5) = 14 --> multiply this out and move the 14 across -----> x^2 +5x -14 = 0

This can be factorised to (x+7)(x-2) = 14 ----> x = -7 or 2

x must be positive so x = 2 (length = 2ft) and width = (x+5) = 7ft

1. x² + 3x + 2 = 4

-1 or -2.

2. Did you mean "The width is 14ft?"
If so
Length:-70ft
Width:-14ft

If you meant length is 14ft, then:
Length:-2.8ft
Width:14ft

x^2 + 3x + 2 = 4
x^2 + 3x + 2 - 4 = 0
x^2 + 3x - 2 = 0
[ x - 2 ][ x - 1 ] = 0


#2
x [5 + x] = 14ft
5x + x^2 = 14
x^2 + 5x -14 = 0
[ x + 7 ][ x - 2 ] = 0
x + 7 = 0 -----> x = - 7
x - 2 = 0 -----> x = 2
two results

length 5ft +(-7) * width -7 =14 ft^2
or 5ft +(2) * width 2 =14 ft^2