SOLUTION: Please help me solve this equation ... {{{4^(x+1)-9(2)^x=-2}}}

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Question 983627: Please help me solve this equation ... 4%5E%28x%2B1%29-9%282%29%5Ex=-2
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
Let us introduce a new variable.

Let  y  be  2%5Ex:   y = 2%5Ex.  Note that 4%5Ex = %282%5Ex%29%5E2 = y%5E2.

Then you can re-write your equation in the form

4y%5E2 - 9y = -2,   or

4y%5E2 - 9y + 2 = 0

It is a quadratic equation.  Solve it using the quadratic formula.

y%5B1%5D = %289+%2B+sqrt%289%5E2+-+4%2A4%2A2%29%29%2F8 = %289%2Bsqrt%2881-32%29%29%2F8 = %289%2Bsqrt%2849%29%29%2F8 = %289%2B7%29%2F8 = 16%2F8 = 2,

y%5B2%5D = %289+-+sqrt%289%5E2+-+4%2A4%2A2%29%29%2F8 = %289-sqrt%2881-32%29%29%2F8 = %289-sqrt%2849%29%29%2F8 = %289-7%29%2F8 = 2%2F8 = 1%2F4.

y%5B1%5D = 2 implies x = 1.

y%5B2%5D = 1%2F4 implies x = -2.

Answer.  There are two solutions:  x = 1  and  x = -2.