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# solve the equation 4^x^2-80=16^x

solve the equation 4^x^2-80=16^x

### 2 Answers by Expert Tutors

Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
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4^x^2-80=16^x  submitted.  I am going to assume
4x2-80=16x or      4x2-16x-80=0 is what is intended
divide by 4 to get x2-4x-20=0 whose solution by formula is
(4±√(16+80))/2=2±2√6
As for the form submitted, graph it.  It's tall skinny slightly lopsided "v"
Bailey S. | Licensed Math Teacher with a Passion for TutoringLicensed Math Teacher with a Passion for...
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Just to clarify, is this the problem you are trying to answer?

4x^2 - 80 = 16x

As in, 4 raised to the power x2 minus 80 equals 16 raised to the power x?

OR

Do you mean:

4x^2 - 80 = 16x

As in, 4 raised to the power x2 -80 equals 16 raised to the power x?

-Bailey S.

This way, there is solution:

4(X^2 -80 ) = 42x,
Then ,   X2 - 80 = 2X

X2 - 2X - 80 =

( X- 10) ( X + 8) = 0

X- 10 = 0    X = 10
X + 8 = 0    X= -8

For:

(4X )2 - 80 = 42x

There is no solution: