# 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.

Word problems leading to quadratic equation.

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.

However we do not adopt negative answers, so our x=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.

Your favorite **Masstisha, **

Adedamola

#ForTheCulture

PS: I hope I have made word problems a bit easier today. I look forward to getting feed-backs from you all. See you, in the next class.