Question
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Answer
The solutions are \( x=2 \) and \( x=3 \).
Solution
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:
\(\left(x-3\right)\left(x-2\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-3=0\\&x-2=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=3\\&x=2\end{align}\)
- step4: Rewrite:
\(x_{1}=2,x_{2}=3\)
The solutions to the equation \(x^{2}-5x+6=0\) are \(x=2\) and \(x=3\).
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Simplify this solution Extra Insights
This equation can be factored as \( (x-2)(x-3)=0 \), giving us the solutions \( x=2 \) and \( x=3 \). Factoring is often a fun way to solve quadratics, allowing you to break them down into simpler linear pieces! When grappling with quadratic equations, a common mistake is overlooking the possibility of factoring. Always check if a quadratic can be expressed as a product of two binomials before heading straight to the quadratic formula! It can save time and lead to clearer insights.
