Answer:
x=− 3/8
x=−2.667
x=−2
4.3 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 =
4
Applying the quadratic formula :
-14 ± √ 4
x = —————
6
Can √ 4 be simplified ?
Yes! The prime factorization of 4 is
2•2
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).
√ 4 = √ 2•2 =
± 2 • √ 1 =
± 2
So now we are looking at:
x = ( -14 ± 2) / 6
Two real solutions:
x =(-14+√4)/6=(-7+)/3= -2.000
or:
x =(-14-√4)/6=(-7-)/3= -2.667
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