Question

use the quadratic formula to solve for x.
\\(9x^2 - x - 2 = 0\\)
(if there is more than one solution, separate them with commas.)
\\(x = \square\\)

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 9\), \(b=-1\), \(c = -2\).

Step2: Recall quadratic formula

Quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).

Step3: Calculate discriminant

Discriminant \(D=b^2-4ac=(-1)^2-4\times9\times(-2)=1 + 72 = 73\).

Step4: Substitute into formula

\(x=\frac{-(-1)\pm\sqrt{73}}{2\times9}=\frac{1\pm\sqrt{73}}{18}\).

Answer:

\(\frac{1 + \sqrt{73}}{18},\frac{1 - \sqrt{73}}{18}\)