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The solutions are \( x=-1 \) and \( x=6 \).
Solución
Solve the equation \( x^{2}-5x-6=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-5x-6=0\)
- step1: Factor the expression:
\(\left(x-6\right)\left(x+1\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-6=0\\&x+1=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=6\\&x=-1\end{align}\)
- step4: Rewrite:
\(x_{1}=-1,x_{2}=6\)
The solutions to the quadratic equation \(x^{2}-5x-6=0\) are \(x=-1\) and \(x=6\).
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Simplifique esta solución Mind Expander
Did you know that when quadratic equations were first tackled, they were often solved using geometrical methods? Ancient Babylonians knew how to deal with these equations around 2000 BC, cleverly using areas and shapes to find their roots! Even though algebraic notation has evolved, the essence of solving these equations remains the same, reminding us of our mathematical roots. Now, let's make it practical! To solve \( x^2 - 5x - 6 = 0 \), you can factor it into \( (x - 6)(x + 1) = 0 \). From there, you'll find the solutions: \( x = 6 \) and \( x = -1 \). A common mistake is forgetting to set each factor to zero, so double-check those steps to avoid missing answers!
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