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. Identify the type of equation given: \(x^2 - 7x + 10 = 0\) is a quadratic equation in standard 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 pairs like (1, 10) and (2, 5), consider their sums with signs to match -7. The pair (-2) and (-5) multiply to 10 and add to -7.
4. Use factoring to rewrite the quadratic as \((x - 2)(x - 5) = 0\).
5. Set each factor equal to zero: \(x - 2 = 0\) and \(x - 5 = 0\), then solve for \(x\) to find the solutions.