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Solve the equation 2^(x+2) - 2^x + 12(2^(x−1)) = 0 for x.

March 17, 2026Mathematics

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Answer

(12 - q)x^{2} - 50

4 steps

Expand the term with the coefficient 10.
$10(x^2 - 5) = 10 \cdot x^2 - 10 \cdot 5 = 10x^2 - 50$
Substitute the expansion into the original expression.
Original expression:
$2x^2 - q x^2 + 10(x^2 - 5)$
Substitute:
$2x^2 - q x^2 + 10x^2 - 50$
Combine the coefficients of the $x^2$ terms.
Coefficients: 2, $-q$ , 10
$2 - q + 10 = 12 - q$
Write the simplified expression.
$(12 - q)x^2 - 50$
(12 - q)x^{2} - 50

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