Respuesta :
Answer:
Two solutions were found :
x =(8-√88)/2=4-√ 22 = -0.690
x =(8+√88)/2=4+√ 22 = 8.690
Step-by-step explanation:
olving x2-8x-6 = 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 = -8
C = -6
Accordingly, B2 - 4AC =
64 - (-24) =
88
Applying the quadratic formula :
8 ± √ 88
x = —————
2
Can √ 88 be simplified ?
Yes! The prime factorization of 88 is
2•2•2•11
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).
√ 88 = √ 2•2•2•11 =
± 2 • √ 22
√ 22 , rounded to 4 decimal digits, is 4.6904
So now we are looking at:
x = ( 8 ± 2 • 4.690 ) / 2
Two real solutions:
x =(8+√88)/2=4+√ 22 = 8.690
or:
x =(8-√88)/2=4-√ 22 = -0.690
Two solutions were found :
x =(8-√88)/2=4-√ 22 = -0.690
x =(8+√88)/2=4+√ 22 = 8.690
