Question

2x^2_13x+18

Answer 1

Two solutions were found :

1. x = 2
2. x = 9/2 = 4.500

Step by step solution : Step 1 : Equation at the end of step 1 : (2x² - 13x) + 18 = 0 Step 2 : Trying to factor by splitting the middle term

Factoring 2x²-13x+18

The first term is, 2x² its coefficient is 2 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +18

Step-1 : Multiply the coefficient of the first term by the constant 2 • 18 = 36

Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is -13 .

	-36	+	-1	=	-37
	-18	+	-2	=	-20
	-12	+	-3	=	-15
	-9	+	-4	=	-13	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -4
2x² - 9x - 4x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-9)
Add up the last 2 terms, pulling out common factors :
2 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(x-2) • (2x-9)
Which is the desired factorization

Equation at the end of step 2 : (2x - 9) • (x - 2) = 0 Step 3 : Theory - Roots of a product :

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

Solve : 2x-9 = 0

Add 9 to both sides of the equation :
2x = 9
Divide both sides of the equation by 2:
x = 9/2 = 4.500

Solving a Single Variable Equation :

Solve : x-2 = 0

Add 2 to both sides of the equation :
x = 2