https://file.aiquickdraw.com/mathbot/file/1726192815881n327xev1.jpg

The image contains a quadratic formula problem. The given quadratic formula is:

\[
x = \frac{-(-1) \pm \sqrt{(1)^2 - 4(2)(-10)}}{2(2)}
\]

We need to evaluate this expression and find the two roots, rounding them to the nearest tenth.

### Step-by-step solution:
1. **Calculate the discriminant**:
   \[
   \Delta = (1)^2 - 4(2)(-10) = 1 + 80 = 81
   \]

2. **Substitute the discriminant into the quadratic formula**:
   \[
   x = \frac{1 \pm \sqrt{81}}{4}
   \]
   Since \(\sqrt{81} = 9\), the formula becomes:
   \[
   x = \frac{1 \pm 9}{4}
   \]

3. **Calculate the two roots**:
   - The first root:
     \[
     x_1 = \frac{1 + 9}{4} = \frac{10}{4} = 2.5
     \]
   - The second root:
     \[
     x_2 = \frac{1 - 9}{4} = \frac{-8}{4} = -2
     \]

### Final answers:
- The smaller root is **-2.0**.
- The larger root is **2.5**.

Would you like more details or explanations?

Here are 5 related questions for practice:
1. How do you calculate the discriminant in the quadratic formula?
2. What does it mean when the discriminant is positive?
3. How would you solve a quadratic equation with a negative discriminant?
4. Can the quadratic formula give complex roots, and how would you identify them?
5. How do you factor a quadratic equation instead of using the formula?

**Tip:** Always check your discriminant before solving a quadratic equation, as it determines the number and type of solutions!

Evaluate the quadratic equation and find the two roots, rounding them to the nearest tenth. The given quadratic formula is: x = (-(-1) ± √((1)^2 - 4(2)(-10)) / (2(2)) )

Learn how to solve a quadratic equation using the quadratic formula. The discriminant is calculated as Δ = b² - 4ac, and the two roots are found by evaluating x = [-b ± √Δ] / 2a. This solution is aimed at students in Grades 8-10.

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