Which would be the most appropriate method to solve the following equation?
$x^2-7x+10=0$

• A.  Factoring
• B. Square-Root Property
• C. Quadratic Formula
• D. Complete the Square

Answer: (A)

Verified step by step guidance

1. Look at the quadratic equation given: \(x^2 - 7x + 10 = 0\). Notice that it is a standard quadratic in the form \(ax^2 + bx + c = 0\) where \(a=1\), \(b=-7\), and \(c=10\).
2. Check if the quadratic can be factored easily by looking for two numbers that multiply to \(c\) (which is 10) and add up to \(b\) (which is -7).
3. Since 10 factors into 5 and 2, and \(-5 + (-2) = -7\), the quadratic can be factored as \((x - 5)(x - 2) = 0\).
4. Because the quadratic factors nicely into integers, factoring is the most straightforward and efficient method to solve this equation.
5. Other methods like the Quadratic Formula, Completing the Square, or the Square-Root Property are more general but not necessary here since factoring works well.