ound to two decimal places $$ x(6 x+1)=2 $$

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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:
   
   $$
   x = 0.50 \quad \text{and} \quad x = -0.67
   $$
The solutions are $$ x = 0.50 $$ and $$ x = -0.67 $$.

ound to two decimal places

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