9x²–7x–2=0

To solve the quadratic equation \(9x^2 - 7x - 2 = 0\), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \(a = 9\), \(b = -7\), and \(c = -2\). 1. Calculate \(b^2 - 4ac\): \[ b^2 - 4ac = (-7)^2 - 4(9)(-2) = 49 + 72 = 121 \] 2. Since \(121\) is a perfect square, we take the square root: \[ \sqrt{121} = 11 \] 3. Now substitute back into the quadratic formula: \[ x = \frac{-(-7) \pm 11}{2(9)} = \frac{7 \pm 11}{18} \] 4. Calculate the two possible values for \(x\): - For \(x_1\): \[ x_1 = \frac{7 + 11}{18} = \frac{