7x2-17x-12=0................................
Answers
Answer:
Step by step solution :
STEP
1
:
Equation at the end of step 1
(7x2 + 17x) - 12 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 7x2+17x-12
The first term is, 7x2 its coefficient is 7 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 7 • -12 = -84
Step-2 : Find two factors of -84 whose sum equals the coefficient of the middle term, which is 17 .
-84 + 1 = -83
-42 + 2 = -40
-28 + 3 = -25
-21 + 4 = -17
-14 + 6 = -8
-12 + 7 = -5
-7 + 12 = 5
-6 + 14 = 8
-4 + 21 = 17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 21
7x2 - 4x + 21x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (7x-4)
Add up the last 2 terms, pulling out common factors :
3 • (7x-4)
Step-5 : Add up the four terms of step 4 :
(x+3) • (7x-4)
Which is the desired factorization
Equation at the end of step
2
:
(7x - 4) • (x + 3) = 0 Solving 7x2+17x-12 = 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 = 7
B = 17
C = -12
Accordingly, B2 - 4AC =
289 - (-336) =
625
Applying the quadratic formula :
-17 ± √ 625
x = ——————
14
Can √ 625 be simplified ?
Yes! The prime factorization of 625 is
5•5•5•5
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 625 = √ 5•5•5•5 =5•5•√ 1 =
± 25 • √ 1 =
± 25
So now we are looking at:
x = ( -17 ± 25) / 14
Two real solutions:
x =(-17+√625)/14=(-17+25)/14= 0.571
or:
x =(-17-√625)/14=(-17-25)/14= -3.000
Two solutions were found :
x = -3
x = 4/7 = 0.571
Answer:
answer is 36
Step-by-step explanation:
7×2=14-17=-3
-3×-12=36