SOLUTION: Solve for x:2 to the power of x^2 -5x = 8 Please show steps Thank you:) Hey thanks for trying I truly do appreciate it however the answer is x = 5 plus/minus √37

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Start with the given equation


Rewrite as


Since the bases are equal, this means that the exponents are equal


So


Set the exponents equal to one another


Subtract 3 from both sides.


Let's use the quadratic formula to solve for x:


Starting with the general quadratic



the general solution using the quadratic equation is:





So lets solve ( notice , , and )




Plug in a=1, b=-5, and c=-3



Negate -5 to get 5



Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because .)



Multiply to get



Combine like terms in the radicand (everything under the square root)



Multiply 2 and 1 to get 2


So now the expression breaks down into two parts

or




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Answer:

So the solutions are

or