Two solutions were found :
- x = -3/2 = -1.500
- 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