×²-7×+10=0 "solve this using quadratic formula"

To solve the quadratic equation \( x^2 - 7x + 10 = 0 \) using the quadratic formula, we follow these steps.

### The quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Where \( ax^2 + bx + c = 0 \) is the standard form of a quadratic equation.

For the given equation \( x^2 - 7x + 10 = 0 \):
- \( a = 1 \)
- \( b = -7 \)
- \( c = 10 \)

### Step-by-step solution:

1. **Calculate the discriminant**:
   \[
   \Delta = b^2 - 4ac
   \]
   \[
   \Delta = (-7)^2 - 4(1)(10) = 49 - 40 = 9
   \]

2. **Apply the quadratic formula**:
   \[
   x = \frac{-(-7) \pm \sqrt{9}}{2(1)}
   \]
   \[
   x = \frac{7 \pm 3}{2}
   \]

3. **Solve for the two possible values of \(x\)**:
   \[
   x_1 = \frac{7 + 3}{2} = \frac{10}{2} = 5
   \]
   \[
   x_2 = \frac{7 - 3}{2} = \frac{4}{2} = 2
   \]

### Final Answer:
The two solutions are \( x_1 = 5 \) and \( x_2 = 2 \).

Would you like more details on any step or further explanation?

Here are 5 related questions:
1. How do you derive the quadratic formula?
2. What happens if the discriminant is negative?
3. Can you solve a quadratic equation by factoring?
4. What is the significance of the discriminant in quadratic equations?
5. How would the quadratic formula change if \( a \neq 1 \)?

**Tip:** The discriminant (\( \Delta = b^2 - 4ac \)) determines the nature of the roots:
- \( \Delta > 0 \): Two real and distinct roots.
- \( \Delta = 0 \): One real and repeated root.
- \( \Delta < 0 \): Two complex roots.

Solve this using quadratic formula: x² - 7x + 10 = 0

This page provides a detailed solution for solving the quadratic equation x² - 7x + 10 using the quadratic formula. It covers core algebraic concepts such as the quadratic formula, the discriminant, and the nature of the roots. Ideal for students in Grades 9-10.

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