Solve the equation 5^(2x+1)=5^-x^2.

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We have to solve 5^(2x+1)=5^-x^2

5^(2x+1)=5^-x^2

As the base is the same we can equate the exponent:

2x + 1 = -x^2

=> x^2 + 2x + 1 = 0

=> (x + 1)^2 = 0

=> x = -1

The required solution is x = -1

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