 # Dear Mathematics students: How to solve WP leading to QE

Dear Mathematics students,

we’re sorry it took us a while to be back but glory to God we’re back now and we’re taking off from where we stopped.

A quadratic equation is an equation in the mold of ax²+bx+c=0.

Example:

The product of two consecutive odd numbers is 323. Find the numbers.

Solution:

First of all, we have to assume that the first number is x. Then the next odd number is x +2.
Therefore x(x+2)=323.
Expanding the bracket, we have: x²+2x=323..
This could also be written as x²+2x-323=0
To solve this, we have to find two factors of -323 whose addition would give us +2.
By testing, we discovered that -17* +19=323 while -17+19=+2.
Therefore we say,
x²-17x+19x-323=0
Factorizing, we have
x(x-17)+19(x-17)=0
(x+19)(x-17)=0
x+19=0 and x-17=0
Therefore, x=-19 or 17.
Then x+2=17+2=19.
Therefore the two numbers are 17 and 19.

Example 2:

If a number is increased by 30, it is less than its square by 30. Find the number.

Solution:

As always, we assume that the number is x.
Increasing it by 12, we have x+12.
The square of x is x² while 12 less than the square is x² -12.
Therefore x+30=x² -12
It will, therefore, become x² -x-12-30=0
x² -x-42=0
Using the factorization method, we examine the factors of -42 that will be added to give us -1.

By testing, we know that the factors are -7 and +6.
Therefore, we have

x² -7x+6x-42=0
x(x-7)+6(x-7)=0
(x+6)(x-7)=0
x+6=0 or x-7=0
x=-6 or +7

Since we don’t reckon with negative answers, x=7.
Check
7+30=7²-12
37=49-12
37=37.