SOLUTION: 8. Solve and Check the Following Equations:
A. 2^(x^2+x) = 64
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Question 113823: 8. Solve and Check the Following Equations:
A. 2^(x^2+x) = 64
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, the exponents are equal. So
Now let's solve for x
Subtract x from both sides
Factor the left side (note: if you need help with factoring, check out this
solver)
Now set each factor equal to zero:
or
or Now solve for x in each case
So our solutions are or
------------------------
Check:
Let's check the solution
Start with the given equation
Plug in
Square -3 to get 9
Add
Raise 2 to the sixth power to get 64. Since both sides of the equation are equal, this solution is verified.
----
Let's check the solution
Start with the given equation
Plug in
Square 2 to get 4
Add
Raise 2 to the sixth power to get 64. Since both sides of the equation are equal, this solution is verified.
So this verifies our solutions and
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