Question
Solve the following equation: \( b^{2}=3 b \) \( \begin{array}{l}\{3,-3\} \\ \text { \{3, 0\} } \\ \text { \{-3, 0\} } \\ \text { \{3\} }\end{array} \)
Ask by Harper Martin. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( b=0 \) and \( b=3 \).
Solution
Solve the equation \( b^{2}=3b \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(b^{2}=3b\)
- step1: Move the expression to the left side:
\(b^{2}-3b=0\)
- step2: Factor the expression:
\(b\left(b-3\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&b-3=0\\&b=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&b=3\\&b=0\end{align}\)
- step5: Rewrite:
\(b_{1}=0,b_{2}=3\)
The solutions to the equation \(b^{2}=3b\) are \(b=0\) and \(b=3\).
Therefore, the solutions are \(\{0,3\}\).
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Simplify this solution Mind Expander
To solve the equation \( b^{2} = 3b \), we can rearrange it to \( b^{2} - 3b = 0 \). Factoring out a \( b \), we get \( b(b - 3) = 0 \). This gives us two solutions: \( b = 0 \) and \( b = 3 \). Therefore, the solution set is \( \{3, 0\} \). Here’s a fun tip: when you see an equation like this, think of it as a sliding puzzle where you’re trying to get \( b \) to one side equal to the other! The zero product property comes in handy here, since if one factor is zero, the entire product equals zero. And just a heads up! A common mistake when factoring is forgetting to set each factor to zero. Always remember: if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \)!
