Solve for x: 4^(x^2+x)-4096=0.
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We have to determine the value of x for the equation: 4^(x^2+x) - 4096 = 0.
4^(x^2+x) - 4096 = 0
=> 4^(x^2+x) = 4096
=> 4^(x^2+x) = 4096
=> 4^(x^2+x) = 4^6
As the base is equal, equate the exponent
=> x^2 + x = 6
=> x^2 + 3x - 2x - 6 = 0
=> x(x + 3) - 2(x + 3) = 0
=> (x - 2)(x + 3) = 0
=> x = 2 and x = -3
The required values are x = 2 and x = -3
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[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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