Which of the following could be SOLVED \( x^{2}-x-6 \) \( x^{2}-9 \) \( 3 x^{2}-2 x-5 \) \( 2 x^{2}-x-6=0 \)

Solve the quadratic equation by following steps: - step0: Solve by factoring: \(2x^{2}-x-6=0\) - step1: Factor the expression: \(\left(x-2\right)\left(2x+3\right)=0\) - step2: Separate into possible cases: \(\begin{align}&x-2=0\\&2x+3=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=2\\&x=-\frac{3}{2}\end{align}\) - step4: Rewrite: \(x_{1}=-\frac{3}{2},x_{2}=2\) Solve the equation \( 3 x^{2}-2 x-5=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(3x^{2}-2x-5=0\) - step1: Factor the expression: \(\left(x+1\right)\left(3x-5\right)=0\) - step2: Separate into possible cases: \(\begin{align}&3x-5=0\\&x+1=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=\frac{5}{3}\\&x=-1\end{align}\) - step4: Rewrite: \(x_{1}=-1,x_{2}=\frac{5}{3}\) Solve the equation \( x^{2}-9=0 \). Solve the quadratic equation by following steps: - step0: Solve using square roots: \(x^{2}-9=0\) - step1: Add or subtract both sides: \(x^{2}=9\) - step2: Simplify the expression: \(x=\pm \sqrt{9}\) - step3: Simplify the expression: \(x=\pm 3\) - step4: Separate into possible cases: \(\begin{align}&x=3\\&x=-3\end{align}\) - step5: Rewrite: \(x_{1}=-3,x_{2}=3\) Solve the equation \( x^{2}-x-6=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}-x-6=0\) - 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: \(x_{1}=-2,x_{2}=3\) Let's solve each of the equations step by step: 1. **Equation:** \( x^{2}-x-6=0 \) - **Solutions:** \( x_{1}=-2 \), \( x_{2}=3 \) 2. **Equation:** \( x^{2}-9=0 \) - **Solutions:** \( x_{1}=-3 \), \( x_{2}=3 \) 3. **Equation:** \( 3x^{2}-2x-5=0 \) - **Solutions:** \( x_{1}=-1 \), \( x_{2}=\frac{5}{3} \) (or approximately \( 1.67 \)) 4. **Equation:** \( 2x^{2}-x-6=0 \) - **Solutions:** \( x_{1}=-\frac{3}{2} \) (or approximately \( -1.5 \)), \( x_{2}=2 \) ### Summary of Solutions: - \( x^{2}-x-6=0 \) has solutions \( x = -2, 3 \) - \( x^{2}-9=0 \) has solutions \( x = -3, 3 \) - \( 3x^{2}-2x-5=0 \) has solutions \( x = -1, \frac{5}{3} \) - \( 2x^{2}-x-6=0 \) has solutions \( x = -\frac{3}{2}, 2 \) All of the given equations can be solved.