[Again, the editing buttons are not working and I cannot
bold the final line. I'll answer the
question.]
4^(x^2+x)-4096=0
We'll
move 4096 to the right side: 4^(x^2+x) = 4096
We'll write
4096 as a power of 4, to create matching bases.
4^(x^2+x) =
4^6
Since the base are matching, we'll apply one to one
property:
x^2+ x = 6
We'll
subtract 6 both sides: x^2 + x - 6 = 0
We'll apply
quadratic formula:
x1 = [-1 + sqrt(1 + 24)]/2 x1 = (-1 +
5)/2 x1 = 2 x2 = (-1-5)/2 x2 = -3
ANSWER: The
solutions of the equation are {-3 ; 2}.
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