Question
Solve for \( y \). Express your answer as an integer or integers or in simplest radical form. \[ -104=4 y^{3}+4 \]
Ask by Cervantes Christensen. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y = -3 \)
Solution
Solve the equation \( -104=4y^{3}+4 \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(-104=4y^{3}+4\)
- step1: Swap the sides:
\(4y^{3}+4=-104\)
- step2: Move the constant to the right side:
\(4y^{3}=-104-4\)
- step3: Subtract the numbers:
\(4y^{3}=-108\)
- step4: Divide both sides:
\(\frac{4y^{3}}{4}=\frac{-108}{4}\)
- step5: Divide the numbers:
\(y^{3}=-27\)
- step6: Simplify the equation:
\(\sqrt[3]{y^{3}}=\sqrt[3]{-27}\)
- step7: Calculate:
\(y=\sqrt[3]{-27}\)
- step8: Simplify the root:
\(y=-3\)
The solution to the equation \( -104=4y^{3}+4 \) is \( y=-3 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve for \( y \), we start by isolating the term with \( y \). We can do this by adding 104 to both sides of the equation: \[ -104 + 104 = 4y^3 + 4 + 104 \] \[ 0 = 4y^3 + 108 \] Next, we simplify this to: \[ 4y^3 = -108 \] We can divide both sides by 4 to further isolate \( y^3 \): \[ y^3 = -27 \] Now, we take the cube root of both sides to solve for \( y \): \[ y = \sqrt[3]{-27} \] Since \(-27\) is a perfect cube, we find: \[ y = -3 \] Thus, the solution is: \[ \boxed{-3} \]
