Question

solve the equation $2x^2 - 5x = 3$ using the method of your choice. what is the positive solution to this equation? (1 point) $x = \square$

Explanation:

Step1: Rewrite in standard form

Rewrite the equation \(2x^2 - 5x = 3\) as \(2x^2 - 5x - 3 = 0\) by subtracting 3 from both sides.

Step2: Factor the quadratic

Factor \(2x^2 - 5x - 3\). We need two numbers that multiply to \(2\times(-3)= -6\) and add to -5. The numbers are -6 and 1. So, we rewrite the middle term:
\(2x^2 - 6x + x - 3 = 0\)
Factor by grouping:
\(2x(x - 3) + 1(x - 3) = 0\)
\((2x + 1)(x - 3) = 0\)

Step3: Solve for x

Set each factor equal to zero:
\(2x + 1 = 0\) or \(x - 3 = 0\)
For \(2x + 1 = 0\), we get \(x = -\frac{1}{2}\). For \(x - 3 = 0\), we get \(x = 3\).

Step4: Identify positive solution

The positive solution is \(x = 3\).

Answer:

\(x = 3\)