X²+5x-14=0

To solve the quadratic equation \(x^2 + 5x - 14 = 0\), you can use the quadratic formula: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \] For the equation \(x^2 + 5x - 14 = 0\), the coefficients are: - \(a = 1\) - \(b = 5\) - \(c = -14\) Plug these values into the quadratic formula: \[ x = \frac{{-5 \pm \sqrt{{5^2 - 4 \times 1 \times (-14)}}}}{2 \times 1} \] \[ x = \frac{{-5 \pm \sqrt{{25 + 56}}}}{2} \] \[ x = \frac{{-5 \pm \sqrt{81}}}{2} \] \[ x = \frac{{-5 \pm 9}}{2} \] This gives the two solutions: \[ x = \frac{{-5 + 9}}{2} = 2 \] \[ x = \frac{{-5 - 9}}{2} = -7 \] The solutions are \(x = 2\) and \(x = -7\).