Solve (2^{(2y + 2)} – 9(2^{y}) = -2).

Solve (2^{(2y + 2)} – 9(2^{y}) = -2).

Explanation

(2^{(2y + 2)} – 9(2^{y}) = -2)

= ((2^{2})(2^{2y}) – 9(2^{y}) = -2)

= (4(2^{y})^{2} – 9(2^{y}) = -2)

Let (2^{y} = x)

(implies 4x^{2} – 9x = -2)

(4x^{2} – 9x + 2 = 0)

(4x^{2} – 8x – x + 2 = 0)

(4x(x – 2) – 1(x – 2) = 0)

((4x – 1)(x – 2) = 0 implies 4x = 1; x = frac{1}{4})

or (x = 2)

If (x = 2^{y} = frac{1}{4} = 2^{-2} implies y = -2)

If (x = 2^{y} = 2^{1} implies y = 1)

(therefore y = -2 ; y = 1)