Solve for $$ x $$ : 11.1 $$ x^{2}+5 x-6=0 $$

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation:

$$
11.1x^{2} + 5x - 6 = 0
$$

we can use the **quadratic formula**, which is:

$$
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
$$

where $$ a = 11.1 $$, $$ b = 5 $$, and $$ c = -6 $$.

### Step 1: Calculate the Discriminant

The discriminant ($$ D $$) is given by:

$$
D = b^{2} - 4ac = 5^{2} - 4(11.1)(-6) = 25 + 266.4 = 291.4
$$

### Step 2: Calculate the Square Root of the Discriminant

$$
\sqrt{D} = \sqrt{291.4} \approx 17.07
$$

### Step 3: Apply the Quadratic Formula

Substitute the values into the formula:

$$
x = \frac{-5 \pm 17.07}{2 \times 11.1} = \frac{-5 \pm 17.07}{22.2}
$$

This gives two solutions:

1. **First Solution:**
   $$
   x = \frac{-5 + 17.07}{22.2} = \frac{12.07}{22.2} \approx 0.543
   $$

2. **Second Solution:**
   $$
   x = \frac{-5 - 17.07}{22.2} = \frac{-22.07}{22.2} \approx -0.994
   $$

### **Final Answer**

The solutions to the equation $$ 11.1x^{2} + 5x - 6 = 0 $$ are:

$$
x \approx 0.543 \quad \text{and} \quad x \approx -0.994
$$
The solutions are $$ x \approx 0.543 $$ and $$ x \approx -0.994 $$.

Solve for \( x \) : 11.1 \( x^{2}+5 x-6=0 \)