Question

solve 2x² - 7x + 6 = 0 by factoring. x = 3 and x = 2, x = -3/2 and x = 2, x = -3 and x = -2, x = -3/2 and x = -2

Explanation:

Step1: Factor the quadratic equation

For the quadratic equation \(2x^{2}-7x + 6=0\), we need to find two numbers that multiply to \(2\times6 = 12\) and add up to - 7. The numbers are - 3 and - 4. So we can rewrite the middle - term: \(2x^{2}-4x-3x + 6 = 0\). Then factor by grouping: \(2x(x - 2)-3(x - 2)=0\), which gives \((2x - 3)(x - 2)=0\).

Step2: Set each factor equal to zero

If \(2x-3 = 0\), then \(2x=3\), and \(x=\frac{3}{2}\). If \(x - 2=0\), then \(x = 2\).

Answer:

\(x=\frac{3}{2}\) and \(x = 2\)