Question

solve for x in the given picture

Answer 1

Given 2^2x + 2^x+2 - 4 * 2^3 = 0.

$2^{2x} - 2^{x+2} - 4 * 2^3 = 0$

$(2^x)^2 - 2^x * 2^2 - 4 * 2^3 = 0$

$(2^x)^2 - 4 * 2^x - 4 * 8 = 0$

$(2^x)^2 - 4(2^x) - 32 = 0$

Let 2^x = a, Then

$(a)^2 - 4a - 32 = 0$

a^2 - 8a + 4a - 32 = 0

a(a - 8) + 4(a - 8) = 0

(a - 8)(a+4) = 0

a = 8, a = -4.

That means,

2^x = 8, 2^x = -4(Not valid).

Therefore 2^x = 8.

2^x = 2^3

x = 3.

Hence,the value of x = 3.


Hope this helps!