Question
6. \( x^{2}+6 x=0 \)
Ask by Maxwell Huang. in Mongolia
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \(x=-6\) and \(x=0\).
Solution
Solve the equation \( x^{2}+6x=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}+6x=0\)
- step1: Factor the expression:
\(x\left(x+6\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x=0\\&x+6=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=0\\&x=-6\end{align}\)
- step4: Rewrite:
\(x_{1}=-6,x_{2}=0\)
The solutions to the equation \(x^{2}+6x=0\) are \(x=-6\) and \(x=0\).
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Simplify this solution Beyond the Answer
To solve the equation \( x^{2} + 6x = 0 \), you can factor it as \( x(x + 6) = 0 \). This gives you two potential solutions: either \( x = 0 \) or \( x + 6 = 0 \), which simplifies to \( x = -6 \). So, your solutions are \( x = 0 \) and \( x = -6 \). Equations like this demonstrate the beauty of factoring! Factoring applies not just in math class; you can find it in various real-life situations such as optimizing areas in gardening or solving practical problems like calculating time savings when reducing costs. Remember, the more you practice, the easier these scenarios become!
