Question

[Lekhanhtai]

x²-13x+42=0

Answer 1

[Cô nàng Thiên Bình dễ thương]

 x²+13x+42=0 

Two solutions were found :

1.  x = -6
2.  x = -7

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²+13x+42 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +13x  its coefficient is  13 .
The last term, "the constant", is  +42 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 42 = 42 

Step-2 : Find two factors of  42  whose sum equals the coefficient of the middle term, which is   13 .

	-42	+	-1	=	-43
	-21	+	-2	=	-23
	-14	+	-3	=	-17
	-7	+	-6	=	-13
	-6	+	-7	=	-13
	-3	+	-14	=	-17
	-2	+	-21	=	-23
	-1	+	-42	=	-43
	1	+	42	=	43
	2	+	21	=	23
	3	+	14	=	17
	6	+	7	=	13	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  6  and  7 
                     x² + 6x + 7x + 42

Step-4 : Add up the first 2 terms, pulling out factors :
                    x • (x+6)
              Add up the last 2 terms, pulling out common factors :
                    7 • (x+6)
Step-5 : Add up the four terms of step 4 :
                    (x+7)  •  (x+6)
             Which is the desired factorization

Equation at the end of step  1  :

(x + 7) • (x + 6) = 0