Answer:
11,-1
Step-by-step explanation:
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Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2-10x-11 = 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 = -10
C = -11
Accordingly, B2 - 4AC =
100 - (-44) =
144
Applying the quadratic formula :
10 ± √ 144
x = —————
2
Can √ 144 be simplified ?
Yes! The prime factorization of 144 is
2•2•2•2•3•3
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).
√ 144 = √ 2•2•2•2•3•3 =2•2•3•√ 1 =
± 12 • √ 1 =
± 12
So now we are looking at:
x = ( 10 ± 12) / 2
Two real solutions:
x =(10+√144)/2=5+6= 11.000
or:
x =(10-√144)/2=5-6= -1.000
Two solutions were found :
x = 11
x = -1
