SOLUTION: Hi, Can someone help me with these problems, as you can see I did try to answer two out of three but since I have been out of school for so long, I not sure of my answers.

Question 243144: Hi,
Can someone help me with these problems, as you can see I did try to answer two out of three but since I have been out of school for so long, I not sure of my answers.

1 solve by factoring and using the principle of zero products
m^2 - 9/16 = 0 I stuck on this one

2. . the product of the page numbers of two facing pages in a book is 506, find the page numbers
My Answer: Not sure it right
Take square root of 506.
It comes out to be 22.4944...
Take the two closest whole numbers; 22 and 23.
22x23= 506.

3. Factoring prime numbers 35+2x-x^2
This is what I got not sure it right.
When you multiply out the brackets you will get x^2+2x-35=0):
(x + 7) (x - 5) = 0
Either:
x + 7 = 0 ..or x - 5 = 0
Therefore:
x = -7 ..or x = 5
Thank you for your help I heard you guys are great.
Tam
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I'm not one of the great ones, but maybe I can help a little.

1. solve by factoring and using the principle of zero products
m^2 - 9/16 = 0 I stuck on this one

m^2 - 9/16 = 0 looks like you can solve by (m-c)*(m+c) so the middle term cancels out.

try c = 3/4 because 3/4 * 3/4 = 9/16

that would make you factors equal to (m-3/4)*(m+3/4)

multiply these factors out and you get:

m^2 + (3/4)*m - (3/4)*m - (3/4)^2

This turns out to be:

m^2 - 9/16 since:

(3/4)^2 = (3^2)/(4^2) = 9/16

looks like you answer is:

(m-(3/4)) * (m+(3/4)

This makes m = (3/4) or m = (-(3/4)

plug these into your original equation and the equations should be true.

your original equation is:

m^2 - 9/16 = 0

let m = 3/4 and you get 9/16 - 9/16 = 0 which is true.

let m = -(3/4) and you get 9/16 - 9/16 = 0 which is true.

the values for x are good.

3. Factoring prime numbers 35+2x-x^2

your answer looks good except for the signs.

your answer is (x+7)*(x-5) = 0 which makes x = -7 and x = 5

if you multiply (x+7) * (x-5) you get x^2 - 5x + 7x - 35 which becomes:

x^2 + 2x - 35 which has the right variables but the wrong signs.

That -x^2 is what usually throws people.

I usually solve these by making the x^2 term positive.

You can do that easily by multiplying both sides of the equation by (-1)

you get:

-x^2 + 2x + 35 = 0 becomes:

x^2 - 2x - 35 = 0

This would be the product of:

(x-7) * (x+5) which would make x = 7 or x = -5

substitute these into your original equation and you will get:

when x = 7, -x^2 + 2x + 35 becomes -49 + 14 + 35 = 0which becomes -49 + 49 = 0 which is true.

when x = -5, -x^2 + 2x + 35 becomes -25 - 10 + 35 = 0 which becomes -35 + 35 = 0 which is true.

not doing what I did, you would have to very careful with the signs as follows:

-x^2 + 2x + 35 = 0

your factors would be (-x - 5) * (x - 7) = 0

multiplying out these factors, you would get:

-x^2 + 7x - 5x + 35 = 0

combine like terms to get:

-x^2 + 2x + 35 = 0

factors are good so you need to solve for x.

-x - 5 = 0 becomes -x = 5

multiply both sides by -1 to get:

x = -5

x - 7 = 0 becomes x = 7

you had the right idea but the signs threw you looks like.

keeping that x^2 term negative is harder to visualize which is why I usually convert the equation to make the x^2 term positive.

confirming the answers are good, however, requires that you go back to the original equation before you modified it just in case you modified it wrong.

2. the product of the page numbers of two facing pages in a book is 506, find the page numbers.

Right off the bat, your answer looks good because the numbers must be in sequence and the only product that will make 506 while the numbers are in sequence seems to be 22*23.

I got the answer a different way, however.

I cheated by using the quadratic formula.

If you let x = the smaller one of the pages, then x+1 has to be the other page.

This makes you equation x * (x+1) = 506

remove parentheses and your equation becomes:

x^2 + x = 506

subtract 506 from both sides of this equation to get:

x^2 + x - 506 = 0

This factors out to be:

(x+23) * (x-22) = 0 which makes x = 22 or x = -23.

Since x can't be -23, then the answer has to be x = 22.

plugging x into the original equation of x * (x+1) = 506 gets you:

22 * 23 = 506 which is true so the answer is good.

Since I didn't know the factors at first, I used the quadratic formula which solves any quadratic equation.

That equation is

The standard form of a quadratic equation is:

ax^2 + bx + c = 0

Your equation of x^2 + x - 506 has terms of:

a = 1
b = 1
c = -502

plugging these into the quadratic formula and solving, I got:

x = 22 or x = -23

Since these are integers, this led me to conclude that the equation could be factored as I confirmed above.

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