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 &#8730;37

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Question 133330: 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 /(2)
Can someone correct this?

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
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

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 &#8730;37

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