Factorisation of :Xsquare +x-50
Factoring x2-x-50
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is 1 .
The last term, "the constant", is -50
Step-1 : Multiply the coefficient of the first term by the constant 1 • -50 = -50
Step-2 : Find two factors of -50 whose sum equals the coefficient of the middle term, which is 1 .
-50 + 1 = -49 -25 + 2 = -23 -10 + 5 = -5 -5 + 10 = 5 -2 + 25 = 23 -1 + 50 = 49
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Solving x2+x-50 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = 1
C = -50
Accordingly, B2 - 4AC =
1 - (-200) =
201
Applying the quadratic formula :
1 ± √ 201
x = —————
2
√ 201 , rounded to 4 decimal digits, is 14.1774
So now we are looking at:
x = ( 1 ± 14.177 ) / 2
Two real solutions:
x =(1+√201)/2= 7.589
or:
x =(1-√201)/2=-6.589
Two solutions were found : - x =(1-√201)/2=-6.589
- x =(1+√201)/2= 7.589
Factoring x2-x-50
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is 1 .
The last term, "the constant", is -50
Step-1 : Multiply the coefficient of the first term by the constant 1 • -50 = -50
Step-2 : Find two factors of -50 whose sum equals the coefficient of the middle term, which is 1 .
| -50 | + | 1 | = | -49 | ||
| -25 | + | 2 | = | -23 | ||
| -10 | + | 5 | = | -5 | ||
| -5 | + | 10 | = | 5 | ||
| -2 | + | 25 | = | 23 | ||
| -1 | + | 50 | = | 49 |
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Solving x2+x-50 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = 1
C = -50
Accordingly, B2 - 4AC =
1 - (-200) =
201
Applying the quadratic formula :
1 ± √ 201
x = —————
2
√ 201 , rounded to 4 decimal digits, is 14.1774
So now we are looking at:
x = ( 1 ± 14.177 ) / 2
Two real solutions:
x =(1+√201)/2= 7.589
or:
x =(1-√201)/2=-6.589
- x =(1-√201)/2=-6.589
- x =(1+√201)/2= 7.589
