Determine the most appropriate method and solve the following equation.
$2x^2-3x-5=0$

• A. Factoring; $x=2.142,x=-0.642$
• B. Square-Root Property; $x=\frac{5}{2},x=1$
• C. Quadratic Formula; $x=\frac{5}{2},x=-1$
• D. Quadratic Formula; $x=1,x=-\frac{5}{2}$

Answer: (C)

Verified step by step guidance

1. First, identify the quadratic equation given: \$2x^2 - 3x - 5 = 0$.
2. Check if the equation can be easily factored by looking for two numbers that multiply to \(2 \times (-5) = -10\) and add to \(-3\). Since such integers are not obvious, factoring is not the best method here.
3. The Square-Root Property applies best when the equation is in the form \(x^2 = k\), which is not the case here because of the linear term \(-3x\).
4. Completing the square is possible but involves extra steps because the coefficient of \(x^2\) is not 1, so it requires dividing the entire equation by 2 first and then completing the square.
5. Therefore, the most straightforward method is to use the Quadratic Formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a=2\), \(b=-3\), and \(c=-5\). Substitute these values into the formula to find the solutions.