SOLUTION: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2 The answer is -1, 1. Please explain and show to me how to get the answer. pls.

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Question 1035074: Given function is 2(raise to the power of 1+2x) - 5(2x)= -2
The answer is -1, 1. Please explain and show to me how to get the answer. pls.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
2^(1+2x)-5(2x)=-2





No clear simple algebraic way to solve from here. x in an exponent and x in a term without exponents.


You might arrange as and make a graph of left side and right side both as functions of x, and identify the intersection.

You say that the answer is supposed to be . Check to see if this value works in the equation.
CHECKING:




The reported answer DOES NOT WORK as a solution.
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
Given function is 2(raise to the power of 1+2x) - 5(2x)= -2
The answer is -1, 1. Please explain and show to me how to get the answer. pls.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1. (-1) is not the root.

2. 1 is the root.

3. There is one more positive root at x ~ 0.9.

4. It may be proved mathematically that there are only two roots, using convexity, for example.

5. The second root might be found approximately/numerically by applying some iteration process.

   Or graphically.

6. I do not see a way to find the second root analytically by means of school math.



Figure. Plot y = .


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