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!