Problem

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

Answer

Expert–verified
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Answer

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

Steps

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

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