To solve the equation \(-5x + 6 = -x^2\), we'll rearrange it into a standard quadratic form, \(ax^2 + bx + c = 0\), and then solve for \(x\).

### Steps:

1. **Rearrange the equation:**

   \[
   -x^2 - 5x + 6 = 0
   \]

2. **Multiply through by \(-1\)** to make the \(x^2\) term positive:

   \[
   x^2 + 5x - 6 = 0
   \]

3. **Factor the quadratic equation:**

   We need to find two numbers that multiply to \(-6\) (the constant term) and add to \(5\) (the coefficient of \(x\)).

   These numbers are \(6\) and \(-1\), so we can factor the equation as:

   \[
   (x + 6)(x - 1) = 0
   \]

4. **Solve for \(x\):**

   Set each factor equal to zero:

   \[
   x + 6 = 0 \quad \text{or} \quad x - 1 = 0
   \]

   \[
   x = -6 \quad \text{or} \quad x = 1
   \]

### Solution:

The solutions to the equation \(-5x + 6 = -x^2\) are \(x = -6\) and \(x = 1\).

Would you like further details or have any questions?

---

Here are 5 related questions for further practice:

1. Solve the quadratic equation \(x^2 - 7x + 10 = 0\).
2. How would you solve \(3x^2 + 5x - 2 = 0\) using the quadratic formula?
3. Factor and solve \(x^2 + 3x - 4 = 0\).
4. What are the solutions for the equation \(x^2 + 2x + 1 = 0\)?
5. How can you solve a quadratic equation by completing the square?

**Tip:** When factoring quadratic equations, always check if the factors multiply to the constant term and add to the coefficient of the linear term.

Learn how to solve the equation -5x + 6 = -x^2 step-by-step with detailed explanations and examples. This problem involves solving quadratic equations through factoring and equation rearrangement. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation