SOLUTION: Solve: 2^x + x = 5 , x is real

Question 1207478: Solve: 2^x + x = 5 , x is real
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
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This equation can not be solved algebraically.

It can be solved approximately, using numerical methods.

Go to web-site www.desmos.com/calculator,
print there y = 2^x + x - 5 and get the plot.

Click where the plot intersects x-axis. You will see the number 1.716.

It is an approximate solution and your answer.

Solved, with explanations.

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        Also, there are supporting thoughts that may help you to feel more confidence.

Notice that left side of the equation is the function, which monotonically increases.

At x= 1,   left side is   2 + 1 = 3.

At x= 2,   left side is   4 + 2 = 6.

It tells you that the solution does exist, that there is only one solution
(= the solution is unique), and that the solution is between 1 and 2.

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