Final answer:
To solve the equation x²+2x-14=0 by completing the square, we add and subtract the square of half the coefficient of x, and then solve for x.
Step-by-step explanation:
To solve the equation x²+2x-14=0 by completing the square, we need to make the left side a perfect square trinomial. To do this, we need to add and subtract the square of half the coefficient of x. In this case, the coefficient of x is 2, so we add and subtract (2/2)², which is 1.
Now the equation becomes x²+2x+1-14-1=0. Rearranging the terms, we get (x+1)²=15. Taking the square root of both sides, we have x+1=±√15. Solving for x, we get x=-1±√15.
Therefore, the solutions to the equation x²+2x-14=0 are x=-1+√15 and x=-1-√15.
Learn more about Solving quadratic equations by completing the square