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Find an equationthat has the given numbers as solutions.
For example, 3 and -2 are solution to x²-x-6=0.

1. 3, -1
2. 1/2, 1/2



What are the four values of x for which (x²-6x-9) =16?



Sagot :

i believe that there are 2 answers to that since it is quadratic not 4..
the highest order of exponent will determine the number of solution
so as to the expression x²-6x-9=16 you will have:
transposing 16 to the left 
x²-6x-9-16=0
x²-6x-25=0
since this can't be factored by mere inspection, then you use quadratic formula
[tex]x = \frac{-b(+-) \sqrt{b^{2}-4ac } }{2a} [/tex]
[tex]x = \frac{-(-6)(+-) \sqrt{ (-6)^{2}-4(1)(-25) } }{2(1)} [/tex]
[tex]x = \frac{6 (+-) \sqrt{136} }{2} [/tex]
[tex]x = \frac{6(+-)2 \sqrt{34} }{2} [/tex]
[tex]x_{1} = 3 +\sqrt{34} [/tex]
[tex] x_{2} = 3 - \sqrt{34} [/tex]
or in decimal
[tex] x_{1}  = 8.83[/tex]
[tex] x_{2} = -2.83[/tex]