Question: User: c) 3 - x^2 = -5x + 7
1. **State the problem:** Solve the equation $$3 - x^2 = -5x + 7$$ for $x$.
2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:
$$3 - x^2 + 5x - 7 = 0$$
3. **Simplify:** Combine like terms:
$$-x^2 + 5x + (3 - 7) = 0$$
$$-x^2 + 5x - 4 = 0$$
4. **Multiply both sides by $-1$** to make the quadratic coefficient positive:
$$\cancel{-1} \times (-x^2 + 5x - 4) = \cancel{-1} \times 0$$
$$x^2 - 5x + 4 = 0$$
5. **Factor the quadratic:** Find two numbers that multiply to $4$ and add to $-5$:
$$(x - 4)(x - 1) = 0$$
6. **Solve for $x$:** Set each factor equal to zero:
$$x - 4 = 0 \Rightarrow x = 4$$
$$x - 1 = 0 \Rightarrow x = 1$$
**Final answer:** The solutions are $$x = 4$$ and $$x = 1$$.