Problem

$2^{2 x}+4 \cdot 2^{x}=-4$

Solution

Step 1 :Let \(y = 2^x\), then the equation becomes \(y^2 + 4y = -4\)

Step 2 :Solve the quadratic equation using the quadratic formula: \(y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where a = 1, b = 4, and c = 4

Step 3 :Calculate the discriminant: \(0\)

Step 4 :Find the solutions for y: \(-2.0, -2.0\)

Step 5 :Substitute back to find the value of x: \(-2.0 = 2^x\)

Step 6 :\(\boxed{\text{There is no real solution for x in the given equation}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8885/

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