Answer:
x =(-5-√45)/2=(-5-3√ 5 )/2= -5.854
x =(-5+√45)/2=(-5+3√ 5 )/2= 0.854
Step-by-step explanation:
2.3 Solving x2+5x-5 = 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 = 5
C = -5
Accordingly, B2 - 4AC =
25 - (-20) =
45
Applying the quadratic formula :
-5 ± √ 45
x = —————
2
Can √ 45 be simplified ?
Yes! The prime factorization of 45 is
3•3•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).
√ 45 = √ 3•3•5 =
± 3 • √ 5
√ 5 , rounded to 4 decimal digits, is 2.2361
So now we are looking at:
x = ( -5 ± 3 • 2.236 ) / 2
Two real solutions:
x =(-5+√45)/2=(-5+3√ 5 )/2= 0.854
or:
x =(-5-√45)/2=(-5-3√ 5 )/2= -5.854
Two solutions were found :
x =(-5-√45)/2=(-5-3√ 5 )/2= -5.854
x =(-5+√45)/2=(-5+3√ 5 )/2= 0.854
