Pregunta
422 What is the solution of \( \sqrt[3]{x+8}=-4 \) ? \( x=-72 \)
Ask by Griffiths Rojas. in the United States
Jan 21,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( x = -72 \)
Solución
Yes, your solution is correct. Here's a step-by-step explanation of how to solve the equation:
\[
\sqrt[3]{x + 8} = -4
\]
**Step 1: Eliminate the Cube Root**
To remove the cube root, you can cube both sides of the equation:
\[
\left( \sqrt[3]{x + 8} \right)^3 = (-4)^3
\]
This simplifies to:
\[
x + 8 = -64
\]
**Step 2: Solve for \( x \)**
Subtract 8 from both sides to isolate \( x \):
\[
x = -64 - 8
\]
\[
x = -72
\]
**Final Answer:**
\[
x = -72
\]
Your solution correctly finds that \( x = -72 \) satisfies the original equation.
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Simplifique esta solución Bonus Knowledge
To solve the equation \( \sqrt[3]{x+8}=-4 \), we first cube both sides to eliminate the cube root, giving us \( x + 8 = (-4)^3 \), which is \( x + 8 = -64 \). Next, we isolate \( x \) by subtracting 8 from both sides, leading to \( x = -64 - 8 \), resulting in \( x = -72 \). So your solution is spot on! Cubing the negative value might seem tricky, but remember: when you raise a negative number to an odd power, the result stays negative. This helpful reminder can prevent common mistakes when handling cube roots and powers in equations!
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