13. Solve the equation $$ x^{3}+7=-20 $$ for $$ x $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ x^{3} + 7 = -20 $$ for $$ x $$, follow these steps:

1. **Start with the original equation:**
   $$
   x^{3} + 7 = -20
   $$

2. **Subtract 7 from both sides to isolate the cubic term:**
   $$
   x^{3} = -20 - 7
   $$
   $$
   x^{3} = -27
   $$

3. **Take the cube root of both sides to solve for $$ x $$:**
   $$
   x = \sqrt[3]{-27}
   $$

4. **Evaluate the cube root:**
   $$
   x = -3
   $$
   *(Because $$(-3)^3 = -27$$)*

**Solution:**
$$
x = -3
$$
$$ x = -3 $$

13. Solve the equation \( x^{3}+7=-20 \) for \( x \)