Questions: Solve the equation. Express your answer in exact simplest form. (5x+66)^(1 / 4) = -3 The solution set is

Solve the equation. Express your answer in exact simplest form. (5x+66)^(1 / 4) = -3 The solution set is
Transcript text: Solve the equation. Express your answer in exact simplest form. \[ (5 x+66)^{1 / 4}=-3 \] The solution set is $\square$
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Solution

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Solution Steps

To solve the equation \((5x + 66)^{1/4} = -3\), we first recognize that the fourth root of a real number cannot be negative. Therefore, there are no real solutions to this equation.

Step 1: Analyze the Equation

We start with the equation

\[ (5x + 66)^{1/4} = -3. \]

Step 2: Consider the Properties of Roots

The fourth root of any real number is defined to be non-negative. Therefore,

\[ (5x + 66)^{1/4} \geq 0. \]

Since \(-3\) is negative, there are no values of \(x\) that can satisfy this equation.

Final Answer

The solution set is \(\boxed{\text{No real solutions}}\).

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