Pregunta
Solve for \( x \) \( x(x-2)=3 \)
Ask by Greene Paul. in South Africa
Mar 15,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = -1 \) or \( x = 3 \)
Solución
Solve the equation \( x(x-2)=3 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x\left(x-2\right)=3\)
- step1: Expand the expression:
\(x^{2}-2x=3\)
- step2: Move the expression to the left side:
\(x^{2}-2x-3=0\)
- step3: Factor the expression:
\(\left(x-3\right)\left(x+1\right)=0\)
- step4: Separate into possible cases:
\(\begin{align}&x-3=0\\&x+1=0\end{align}\)
- step5: Solve the equation:
\(\begin{align}&x=3\\&x=-1\end{align}\)
- step6: Rewrite:
\(x_{1}=-1,x_{2}=3\)
The solutions to the equation \(x(x-2)=3\) are \(x=-1\) and \(x=3\).
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Simplifique esta solución Mind Expander
To solve the equation \( x(x-2)=3 \), we first rearrange the equation into standard form: \[ x^2 - 2x - 3 = 0 \] Next, we can factor the quadratic: \[ (x - 3)(x + 1) = 0 \] Setting each factor to zero gives us the possible solutions: \[ x - 3 = 0 \quad \text{or} \quad x + 1 = 0 \] This leads to: \[ x = 3 \quad \text{or} \quad x = -1 \] Thus, the solutions for \( x \) are \( x = 3 \) and \( x = -1 \).
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