Answer:
x =(14-√388)/6=(7-√ 97 )/3= -0.950
x =(14+√388)/6=(7+√ 97 )/3= 5.616
explanation: Equation at the end of step 1 :
(3x2 - 14x) - 16 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2-14x-16
Equation at the end of step 2 :
3x2 - 14x - 16 = 0
Step 3 :
Parabola, Finding the Vertex :
3.1 Find the Vertex of y = 3x2-14x-16
Add 7/3 to both sides to obtain:
x = 7/3 + √ 97/9
Since a square root has two values, one positive and the other negative
x2 - (14/3)x - (16/3) = 0
has two solutions:
x = 7/3 + √ 97/9
or
x = 7/3 - √ 97/9
Note that √ 97/9 can be written as
√ 97 / √ 9 which is √ 97 / 3
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving 3x2-14x-16 = 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 = 3
B = -14
C = -16
Accordingly, B2 - 4AC =
196 - (-192) =
388
Applying the quadratic formula :
14 ± √ 388
x = ——————
6
Can √ 388 be simplified ?
Yes! The prime factorization of 388 is
2•2•97
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).
√ 388 = √ 2•2•97 =
± 2 • √ 97
