ound to two decimal places \[ x(6 x+1)=2 \]

To solve the equation \( x(6x + 1) = 2 \) and round the solutions to two decimal places, follow these steps: 1. **Expand the Equation:** \[ x(6x + 1) = 2 \\ 6x^2 + x = 2 \\ 6x^2 + x - 2 = 0 \] 2. **Identify the Coefficients:** The quadratic equation is in the form \( ax^2 + bx + c = 0 \), where: - \( a = 6 \) - \( b = 1 \) - \( c = -2 \) 3. **Use the Quadratic Formula:** The solutions for \( x \) are given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Plugging in the values: \[ x = \frac{-1 \pm \sqrt{1^2 - 4(6)(-2)}}{2(6)} \\ x = \frac{-1 \pm \sqrt{1 + 48}}{12} \\ x = \frac{-1 \pm \sqrt{49}}{12} \\ x = \frac{-1 \pm 7}{12} \] 4. **Calculate the Solutions:** - **First Solution:** \[ x = \frac{-1 + 7}{12} = \frac{6}{12} = 0.5 \] Rounded to two decimal places: \( x = 0.50 \) - **Second Solution:** \[ x = \frac{-1 - 7}{12} = \frac{-8}{12} = -0.6666\ldots \] Rounded to two decimal places: \( x = -0.67 \) 5. **Final Answer:** The solutions to the equation \( x(6x + 1) = 2 \) rounded to two decimal places are: \[ x = 0.50 \quad \text{and} \quad x = -0.67 \]