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 \(x = -7\).