SOLUTION: I need help on finding all real solutions for 2^2x-24(2^x)=256

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Question 6448: I need help on finding all real solutions for 2^2x-24(2^x)=256
Answer by ichudov(507)   (Show Source): You can put this solution on YOUR website!
Use . is , or .
y^2-24y-256=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1600 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 32, -8. Here's your graph:


so, we have 2^x = 32, -8. x=5 makes 2^x equal to 32. Nothing could make 2^x equal to -8. So the answer is x=5.
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