Question
What are the solution(s) to the equation \( \sqrt[3]{43 x+125}+20=28 \) ?
Ask by Logan Gross. in the United States
Jan 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 9 \)
Solution
To solve the equation:
\[
\sqrt[3]{43x + 125} + 20 = 28
\]
**Step 1: Isolate the Cube Root**
Subtract 20 from both sides:
\[
\sqrt[3]{43x + 125} = 28 - 20
\]
\[
\sqrt[3]{43x + 125} = 8
\]
**Step 2: Eliminate the Cube Root**
Cube both sides to eliminate the cube root:
\[
(\sqrt[3]{43x + 125})^3 = 8^3
\]
\[
43x + 125 = 512
\]
**Step 3: Solve for \( x \)**
Subtract 125 from both sides:
\[
43x = 512 - 125
\]
\[
43x = 387
\]
Divide both sides by 43:
\[
x = \frac{387}{43}
\]
\[
x = 9
\]
**Solution:**
\[
x = 9
\]
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Simplify this solution Extra Insights
To solve the equation \( \sqrt[3]{43x + 125} + 20 = 28 \), we start by isolating the cube root: \[ \sqrt[3]{43x + 125} = 28 - 20 \] \[ \sqrt[3]{43x + 125} = 8 \] Next, we eliminate the cube root by cubing both sides: \[ 43x + 125 = 8^3 \] Calculating \( 8^3 \): \[ 8^3 = 512 \] So, we rewrite the equation as: \[ 43x + 125 = 512 \] Now, we solve for \( x \) by subtracting 125 from both sides: \[ 43x = 512 - 125 \] \[ 43x = 387 \] Finally, we divide both sides by 43 to find \( x \): \[ x = \frac{387}{43} = 9 \] Thus, the solution to the equation is \[ x = 9. \]
