What are the x intercepts of the equation y=2x^2+3x-9

Question

Find the x intercepts of this equation

Answer 1

Two solutions were found :

1.  x = -3/2 = -1.500
2.  x = 3

 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     2*x^2-(3*x+9)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

2x

2 - (3x + 9) = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x2-3x-9 

The first term is,  2x2  its coefficient is  2 .
The middle term is,  -3x  its coefficient is  -3 .
The last term, "the constant", is  -9 
Step-1 : Multiply the coefficient of the first term by the constant   2 • -9 = -18 
Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -3 .

	-18	+	1	=	-17
	-9	+	2	=	-7
	-6	+	3	=	-3	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  3 
                     2x2 - 6x + 3x - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (x-3)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-3)
Step-5 : Add up the four terms of step 4 :
                    (2x+3)  •  (x-3)
             Which is the desired factorization