SOLUTION: Can you please help with these word problems I am terrible at word problems. I listed the problems below along with what I could figure out. Thanks in advance. Solving Quadratic

Question 248262: Can you please help with these word problems I am terrible at word problems. I listed the problems below along with what I could figure out. Thanks in advance.
Solving Quadratic Equations by Factoring
1. Address book. The perimeter of the cover of an address book
is 14 inches, and the diagonal measures 5 inches. What are
the length and width of the cover?
x^2+14=5^2
x^2+x^2+14=25
2x^2+14=25
-14=-14
2x^2=11 don't know if this is right thus far and where to go from here.

2. Throwing a wrench. An angry construction worker throws
his wrench downward from a height of 128 feet with an
initial velocity of 32 feet per second. The height of the
wrench above the ground after t seconds is given
by S(t)-16t^2-32t+128.
-16(t+4)(t-2)is what I have so far!!
a) What is the height of the wrench after 1 second?
b) How long does it take for the wrench to reach the
ground?

Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solving Quadratic Equations by Factoring
1. Address book. The perimeter of the cover of an address book
is 14 inches, and the diagonal measures 5 inches. What are
the length and width of the cover?
---
Equations:
P = 2(L + W)
L^2 + W^2 = 5^2
---------------------
7 = L + W
L = 7-W
----------------
Substitute for "L" and solve for "W":
(7-W)^2 + W^2 = 25
49 - 2W + 2W^2 = 25
2w^2 - 2w + 24 = 0
w^2 - w + 12 = 0
(w-4)(w+3) = 0
Positive solution:
W = 4 (width)
---
Then L = 3 (length)
=========================
2. Throwing a wrench. An angry construction worker throws
his wrench downward from a height of 128 feet with an
initial velocity of 32 feet per second. The height of the
wrench above the ground after t seconds is given
by S(t)= -16t^2-32t+128.
-16(t+4)(t-2)is what I have so far!!
a) What is the height of the wrench after 1 second?
Solve S(1) = -16-32+128 = -48+128 = 80 ft.
------------------------------------------------
b) How long does it take for the wrench to reach the
ground?
When the wrench is on the ground S(t) is zero.
So -16t^2-32t+128 = 0
-16(t+4)(t-2) = 0
Positive solution:
t = 2 seconds
======================
Cheers,
Stan H.

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
2x^2=11
don't know if this is right thus far and where to go from here.
if this were right you would divide by 2
x^2=11/2
then get sqrt
x=sqrt(11/2)

Address book. The perimeter of the cover of an address book
is 14 inches, and the diagonal measures 5 inches. What are
the length and width of the cover?
It appears you are too anxious to do the problems that you aren't reading them.
what is 14?
14 is the perimeter.
What is the perimeter.
Someone who walks the perimeter of the ranch walks around the edge of the ranch.
so the perimeter is the walk around the rectangle or circle. since it is an address book It is a rectangle maybe a square.
In either case P=2L+2W
in the case of a square L=W
so we have now 2L+2W=14
2(L=W)=14
l+w=7
the diagonal measures 5 inches
What is the diagonal of rectangle?
It is the hypotenuse of the right triangle formed by the sides L and W
so we know that W=7-L
using the Pythagorean theorem a^2+b^2=c^2
but we have W^2+L^2=5^5
and W=7-L
substitute 7-L for W
and we get and that (7-L)^2+L^2=5^2
multiply it out using FOIL
(7-L)(7-L)
first
7*7=7^2=49
outside
7*-L
inside
7*-L
last
-L*-L=L^2
putting it altogether and rearranging to normal format
L^2+L^2-14L+49=25
2L^2-14L+24=0
divide by 2
L^2-7L+12=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, 3. Here's your graph:

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