X^ 2+2 x=14

Step 1 ：We are given the quadratic equation \(x^2 + 2x = 14\).

Step 2 ：We can rewrite this equation in the standard form of a quadratic equation, which is \(ax^2 + bx + c = 0\). In this case, we have \(a = 1\), \(b = 2\), and \(c = -14\).

Step 3 ：We can solve this equation using the quadratic formula, which is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 4 ：First, we calculate the discriminant, \(D = b^2 - 4ac\). Substituting the values of \(a\), \(b\), and \(c\), we get \(D = 60\).

Step 5 ：Next, we substitute the values of \(a\), \(b\), and \(D\) into the quadratic formula to find the solutions. The solutions are \(x = \frac{-b \pm \sqrt{D}}{2a}\).

Step 6 ：Substituting the values, we get two solutions: \(x = -4.872983346207417\) and \(x = 2.872983346207417\).

Step 7 ：Final Answer: The solutions to the equation are \(\boxed{-4.872983346207417}\) and \(\boxed{2.872983346207417}\).