Question

resolva a a equação.
2^{-5x-x^2}= 1/64

Answer 1

$2^{-5x- x^{2} } = \frac{1}{64} \\ 2^{-5x- x^{2} } = \frac{1}{ 2^{6} } \\ 2^{-5x- x^{2} } = 2^{-6}$
-5x-x²=-6
-x²-5x+6=0
x²+5x-6=0

$x= \frac{-b+- \sqrt{ b^{2}-4ac } }{2a} = \frac{-5+- \sqrt{ 5^{2}-4(1)(-6) } }{2(1)}= \frac{-5+- \sqrt{ 25+24 } }{2} \\ \frac{-5+- \sqrt{ 49 } }{2}= \frac{-5+- 7 }{2}$
x1=(-5+7)/2 = 2/2 = 1
x2=(-5-7)/2 = -12/2 = -6

resp: x= 1 ou x=-6